FA-5544 / Number theory / Member archive

Modular multiplicative inverse · case 04

Fermat inversion is used without a prime-modulus precondition.

Member previewVariant 4 · 3 implementations · 4 checks per implementation

Case contract

Integer inputs; n is positive unless a zero or negative fixture explicitly extends that operation. A modulus is greater than one; p is prime; exponent k may be signed when an inverse exists. a may be signed; return the least nonnegative inverse modulo m or None if gcd(a,m)!=1. Exact operational definition: pow(a,-1,m) if math.gcd(a,m)==1 else None

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Number theory results depend on the stated convention.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
fixture 1: (3, 10)	`1`	`7`	Failed

MEMBER ARCHIVE

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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