FA-5574 / Number theory / Member archive

Digital root base ten · case 04

A zero remainder represents nine for nonzero multiples.

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. n is any signed integer; repeatedly sum magnitude digits until one remains, preserving zero. Exact operational definition: 0 if n==0 else 1+(abs(n)-1)%9

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 2: (18,)	`0`	`9`	Failed

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