Open Research Index

Pascal Minus-One GCD

John Fairfax-Ball

Palomar Registrypalomar/PALOMAR-2026-09-25-000017Sep 25, 2026math.NTscore 0

A Lean 4 formalization of p-adic valuations for the restricted binomial gcd G(N;m) = gcd{C(N,k) : 0 < k < N, m divides k}. The principal submitted result gives the complete valuation formula for primes p congruent to -1 modulo m, including the mixed-parity digit-sum branch and the exceptional p = m - 1 valuation-2 case. The repository also proves the complementary p congruent to 1 branch, a prime-power scaling reduction, and complete prime-by-prime formulas for m = 3, 4, and 6.

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