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R0017-09088 · q-20261013-advance-20261018-r05-modular-congruence-0013
Fix modulus n=0, natural a=43, b=72. Give (n, a, b, n>0?, [a mod n,b mod n] or not-evaluated, congruent? or not-evaluated). This entry excludes zero-modulus conventions.
G001 — Fix modulus n=0, natural a=43, b=72. Give (n, a, b, n>0?, [a mod n,b mod n] or not-evaluated, congruent? or not-evaluated). This entry excludes zero-modulus conventions.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
fixed natural modulus candidate=0
After
positive modulus=No
Conditions: none
Congruence compares remainders at one positive modulus,not numerical equality.Multiplicative preservation does not permit unconditional cancellation of a common factor.
Rule: fixed_positive_modulus_scope · Uses: G001
Before
n=0;a=43;b=72
After
remainders=not evaluated;congruence=not evaluated
Conditions: none
When the modulus is not positive,both remainders and congruence remain unevaluated.Do not manufacture a truth value from an API default.
Rule: zero_modulus_no_remainder_evaluation · Uses: G001, S001
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.(0, 43, 72, No, not-evaluated, not-evaluated)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 9324abf89687101462c303c43169606a8af4d1dc9bd1aa99b7773c5a3519bb41candidate record SHA-256: e7709316dd2fc8c0fbf6def181cb0d9e7fbed53fb17359561f180b88467e6db6semantic review receipt SHA-256: abad28564830bb9b6ef069ca5a1aa128ce7b1a67a5cb8fe6d868a06db73bcfb8question-first witness SHA-256: 43126988479968837abe086263dac1b24c37463ad80e00d2e280a7b8e9036a04Lean: NOT_RUN · human review: NOT_PERFORMED