Signed Extended Euclid, Normalized Inverses and Nonunit Boundaries
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batch-20261014-advance-20261103-r07-modular-inverse-foundations · 2026-10-14 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
1. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=27≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 27, 1, Yes, 14)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 27, 1, Yes, 14).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
2. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=3 and modulus n=28≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(3, 28, 1, Yes, 19)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (3, 28, 1, Yes, 19).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
3. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=29≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 29, 1, Yes, 15)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 29, 1, Yes, 15).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
4. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=7 and modulus n=30≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(7, 30, 1, Yes, 13)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (7, 30, 1, Yes, 13).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
5. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=31≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 31, 1, Yes, 16)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 31, 1, Yes, 16).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
6. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=3 and modulus n=32≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(3, 32, 1, Yes, 11)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (3, 32, 1, Yes, 11).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
7. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=33≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 33, 1, Yes, 17)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 33, 1, Yes, 17).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
8. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=3 and modulus n=34≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(3, 34, 1, Yes, 23)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (3, 34, 1, Yes, 23).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
9. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=35≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 35, 1, Yes, 18)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 35, 1, Yes, 18).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
10. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=5 and modulus n=36≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(5, 36, 1, Yes, 29)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (5, 36, 1, Yes, 29).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
11. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=37≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 37, 1, Yes, 19)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 37, 1, Yes, 19).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
12. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=3 and modulus n=38≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(3, 38, 1, Yes, 13)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (3, 38, 1, Yes, 13).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
13. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=39≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 39, 1, Yes, 20)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 39, 1, Yes, 20).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
14. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=3 and modulus n=40≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(3, 40, 1, Yes, 27)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (3, 40, 1, Yes, 27).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
15. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=41≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 41, 1, Yes, 21)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 41, 1, Yes, 21).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
16. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=5 and modulus n=42≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(5, 42, 1, Yes, 17)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (5, 42, 1, Yes, 17).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
17. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=43≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 43, 1, Yes, 22)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 43, 1, Yes, 22).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
18. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=3 and modulus n=44≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(3, 44, 1, Yes, 15)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (3, 44, 1, Yes, 15).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
19. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=45≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 45, 1, Yes, 23)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 45, 1, Yes, 23).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
20. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=3 and modulus n=46≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(3, 46, 1, Yes, 31)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (3, 46, 1, Yes, 31).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
21. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=47≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 47, 1, Yes, 24)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 47, 1, Yes, 24).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
22. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=5 and modulus n=48≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(5, 48, 1, Yes, 29)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (5, 48, 1, Yes, 29).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
23. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=49≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 49, 1, Yes, 25)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 49, 1, Yes, 25).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
24. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=3 and modulus n=50≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(3, 50, 1, Yes, 17)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (3, 50, 1, Yes, 17).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
25. A Modular Inverse Exists Exactly for a Unit
Use the original signed integer a=2 and modulus n=51≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,exists?,inverse), with inverse=null for a nonunit.
View answer and explanation
(2, 51, 1, Yes, 26)
Compute the exact gcd first. A unit obtains its normalized inverse from the Bezout coefficient; a gcd greater than one excludes an inverse modulo n. The exact result, retaining the requested order, is (2, 51, 1, Yes, 26).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-existence · candidate
26. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=27≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 27, 1, -13, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 27, 1, -13, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
27. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=3 and modulus n=28≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(3, 28, 1, -9, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (3, 28, 1, -9, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
28. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=29≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 29, 1, -14, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 29, 1, -14, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
29. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=7 and modulus n=30≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(7, 30, 1, 13, -3, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (7, 30, 1, 13, -3, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
30. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=31≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 31, 1, -15, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 31, 1, -15, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
31. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=3 and modulus n=32≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(3, 32, 1, 11, -1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (3, 32, 1, 11, -1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
32. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=33≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 33, 1, -16, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 33, 1, -16, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
33. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=3 and modulus n=34≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(3, 34, 1, -11, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (3, 34, 1, -11, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
34. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=35≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 35, 1, -17, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 35, 1, -17, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
35. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=5 and modulus n=36≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(5, 36, 1, -7, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (5, 36, 1, -7, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
36. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=37≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 37, 1, -18, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 37, 1, -18, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
37. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=3 and modulus n=38≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(3, 38, 1, 13, -1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (3, 38, 1, 13, -1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
38. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=39≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 39, 1, -19, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 39, 1, -19, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
39. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=3 and modulus n=40≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(3, 40, 1, -13, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (3, 40, 1, -13, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
40. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=41≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 41, 1, -20, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 41, 1, -20, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
41. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=5 and modulus n=42≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(5, 42, 1, 17, -2, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (5, 42, 1, 17, -2, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
42. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=43≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 43, 1, -21, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 43, 1, -21, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
43. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=3 and modulus n=44≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(3, 44, 1, 15, -1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (3, 44, 1, 15, -1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
44. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=45≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 45, 1, -22, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 45, 1, -22, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
45. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=3 and modulus n=46≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(3, 46, 1, -15, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (3, 46, 1, -15, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
46. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=47≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 47, 1, -23, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 47, 1, -23, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
47. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=5 and modulus n=48≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(5, 48, 1, -19, 2, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (5, 48, 1, -19, 2, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
48. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=49≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 49, 1, -24, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 49, 1, -24, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
49. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=3 and modulus n=50≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(3, 50, 1, 17, -1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (3, 50, 1, 17, -1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
50. Keep Signed Bezout Coefficients and Verify the Integer Identity
Use the original signed integer a=2 and modulus n=51≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Give (a,n,gcd,x,y,bezout_value,classification), retaining the coefficients returned by exact Euclidean steps on |a| and n, with the sign of a restored in x.
View answer and explanation
(2, 51, 1, -25, 1, 1, Bezout_equals_one)
Substitute the signed coefficients into a*x+n*y. The value is the nonnegative gcd. Classification is Bezout_equals_one or nonunit_Bezout_gcd; the coefficients are witnesses, not a unique pair of integers. The exact result, retaining the requested order, is (2, 51, 1, -25, 1, 1, Bezout_equals_one).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-extended-euclid · candidate
51. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=27≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 27, 14, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 27, 14, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
52. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=3 and modulus n=28≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(3, 28, 19, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (3, 28, 19, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
53. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=29≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 29, 15, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 29, 15, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
54. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=7 and modulus n=30≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(7, 30, 13, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (7, 30, 13, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
55. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=31≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 31, 16, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 31, 16, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
56. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=3 and modulus n=32≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(3, 32, 11, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (3, 32, 11, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
57. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=33≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 33, 17, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 33, 17, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
58. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=3 and modulus n=34≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(3, 34, 23, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (3, 34, 23, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
59. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=35≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 35, 18, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 35, 18, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
60. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=5 and modulus n=36≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(5, 36, 29, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (5, 36, 29, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
61. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=37≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 37, 19, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 37, 19, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
62. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=3 and modulus n=38≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(3, 38, 13, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (3, 38, 13, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
63. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=39≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 39, 20, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 39, 20, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
64. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=3 and modulus n=40≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(3, 40, 27, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (3, 40, 27, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
65. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=41≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 41, 21, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 41, 21, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
66. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=5 and modulus n=42≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(5, 42, 17, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (5, 42, 17, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
67. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=43≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 43, 22, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 43, 22, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
68. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=3 and modulus n=44≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(3, 44, 15, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (3, 44, 15, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
69. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=45≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 45, 23, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 45, 23, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
70. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=3 and modulus n=46≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(3, 46, 31, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (3, 46, 31, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
71. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=47≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 47, 24, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 47, 24, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
72. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=5 and modulus n=48≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(5, 48, 29, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (5, 48, 29, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
73. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=49≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 49, 25, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 49, 25, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
74. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=3 and modulus n=50≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(3, 50, 17, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (3, 50, 17, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
75. Normalize the Inverse Representative, Not the Bezout Coefficients
Use the original signed integer a=2 and modulus n=51≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)=1. Give (a,n,inverse,product_mod_n,valid?,unique_modulo_n).
View answer and explanation
(2, 51, 26, 1, Yes, unique_modulo_n)
Reduce the exact Bezout x modulo n and check a*inverse≡1 mod n. The normalized representative is unique in [0,n), while infinitely many congruent integer representatives exist. The exact result, retaining the requested order, is (2, 51, 26, 1, Yes, unique_modulo_n).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-normalized-inverse · candidate
76. A Nonunit Has No Modular Inverse
Use the original signed integer a=2 and modulus n=4≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(2, 4, 2, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (2, 4, 2, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
77. A Nonunit Has No Modular Inverse
Use the original signed integer a=3 and modulus n=6≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(3, 6, 3, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (3, 6, 3, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
78. A Nonunit Has No Modular Inverse
Use the original signed integer a=4 and modulus n=8≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(4, 8, 4, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (4, 8, 4, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
79. A Nonunit Has No Modular Inverse
Use the original signed integer a=5 and modulus n=10≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(5, 10, 5, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (5, 10, 5, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
80. A Nonunit Has No Modular Inverse
Use the original signed integer a=6 and modulus n=12≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(6, 12, 6, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (6, 12, 6, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
81. A Nonunit Has No Modular Inverse
Use the original signed integer a=7 and modulus n=14≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(7, 14, 7, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (7, 14, 7, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
82. A Nonunit Has No Modular Inverse
Use the original signed integer a=8 and modulus n=16≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(8, 16, 8, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (8, 16, 8, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
83. A Nonunit Has No Modular Inverse
Use the original signed integer a=9 and modulus n=18≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(9, 18, 9, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (9, 18, 9, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
84. A Nonunit Has No Modular Inverse
Use the original signed integer a=10 and modulus n=20≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(10, 20, 10, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (10, 20, 10, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
85. A Nonunit Has No Modular Inverse
Use the original signed integer a=11 and modulus n=22≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(11, 22, 11, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (11, 22, 11, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
86. A Nonunit Has No Modular Inverse
Use the original signed integer a=12 and modulus n=24≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(12, 24, 12, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (12, 24, 12, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
87. A Nonunit Has No Modular Inverse
Use the original signed integer a=13 and modulus n=26≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(13, 26, 13, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (13, 26, 13, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
88. A Nonunit Has No Modular Inverse
Use the original signed integer a=14 and modulus n=28≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(14, 28, 14, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (14, 28, 14, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
89. A Nonunit Has No Modular Inverse
Use the original signed integer a=15 and modulus n=30≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(15, 30, 15, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (15, 30, 15, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
90. A Nonunit Has No Modular Inverse
Use the original signed integer a=16 and modulus n=32≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(16, 32, 16, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (16, 32, 16, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
91. A Nonunit Has No Modular Inverse
Use the original signed integer a=17 and modulus n=34≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(17, 34, 17, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (17, 34, 17, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
92. A Nonunit Has No Modular Inverse
Use the original signed integer a=18 and modulus n=36≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(18, 36, 18, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (18, 36, 18, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
93. A Nonunit Has No Modular Inverse
Use the original signed integer a=19 and modulus n=38≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(19, 38, 19, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (19, 38, 19, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
94. A Nonunit Has No Modular Inverse
Use the original signed integer a=20 and modulus n=40≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(20, 40, 20, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (20, 40, 20, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
95. A Nonunit Has No Modular Inverse
Use the original signed integer a=21 and modulus n=42≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(21, 42, 21, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (21, 42, 21, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
96. A Nonunit Has No Modular Inverse
Use the original signed integer a=22 and modulus n=44≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(22, 44, 22, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (22, 44, 22, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
97. A Nonunit Has No Modular Inverse
Use the original signed integer a=23 and modulus n=46≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(23, 46, 23, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (23, 46, 23, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
98. A Nonunit Has No Modular Inverse
Use the original signed integer a=24 and modulus n=48≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(24, 48, 24, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (24, 48, 24, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
99. A Nonunit Has No Modular Inverse
Use the original signed integer a=25 and modulus n=50≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(25, 50, 25, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (25, 50, 25, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
100. A Nonunit Has No Modular Inverse
Use the original signed integer a=26 and modulus n=52≥2. Exact extended Euclid gives nonnegative g=gcd(a,n) and signed coefficients x,y satisfying a*x+n*y=g. An inverse exists exactly when g=1; normalize its representative to 0≤inverse<n. Uniqueness means one residue class modulo n, not a unique integer representative. This family excludes moduli 0 and 1 and does not use approximate division. Require gcd(a,n)>1. Give (a,n,gcd,inverse,exists?,nonunit_has_no_modular_inverse), with inverse=null.
View answer and explanation
(26, 52, 26, null, No, nonunit_has_no_modular_inverse)
A product congruent to one would force the gcd to divide one, contradicting this nonunit premise. Do not attempt ordinary or floating-point division, and reject a unit supplied to this nonunit-boundary family. The exact result, retaining the requested order, is (26, 52, 26, null, No, nonunit_has_no_modular_inverse).
Reviewed step-by-step derivation
Modular inverse · qf-mod34-modinv-nonunit-boundary · candidate
Canonical question JSONL · English JSONL · Validation report