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arXiv · 2609.37754

Restricted Binomial GCDs at Primes Congruent to -1

John Fairfax-Ball
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Abstract

For integers $m\geq 2$ and $m\mid N$, let $G(N;m)=\gcd\{\binom{N}{k}:0 m$ subcases, but not the mixed-parity branch or the $p=m-1$ regime. The theorem, its plus-one companion, a scaling reduction, and the $m=3,4,6$ specializations have been formalized in Lean 4 / Mathlib.

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John Fairfax-Ball. 2026-09-29. Restricted Binomial GCDs at Primes Congruent to -1. https://arxiv.org/abs/2609.37754

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