Restricted Binomial GCDs at Primes Congruent to -1

Source 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.