Question 27701: Wilson Domain, Finite Testing, Fermat Comparison and the p=2 Exception Stay Separate

Original question and givens

Use mode=p2_self_inverse and exact integer n=2. Give (mode, p, self_inverse_residues, modular_identity, distinct_residue_scope, exception_qualified).

• G001 — Use mode=p2_self_inverse and exact integer n=2. Give (mode, p, self_inverse_residues, modular_identity, distinct_residue_scope, exception_qualified).

Definition and scope

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.

• mko-wilson-theorem

Step-by-step derivation

source roles = [wilson-boundary]

derived = [[mode, p, self_inverse_residues, modular_identity, distinct_residue_scope, exception_qualified]]

source roles = [2]

derived = [[1], 1_equals_minus_1_mod_2, Yes]

Reverse checks

• S002 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S001 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.

Result

(p2_self_inverse, 2, [1], 1_equals_minus_1_mod_2, one_not_two_distinct_self_inverse_residues, Yes)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.