Open Research Index

Pascal Extremes

John Fairfax-Ball

Palomar Registrypalomar/PALOMAR-2026-09-30-000033Sep 30, 2026math.NTscore 0

A Lean 4 formalisation of sharp p-adic extremal behaviour for the restricted binomial gcd G(N;m) = gcd{C(N,k) : 0 = 2 with p not dividing m, it proves that the maximum of v_p(G(N;m)) over admissible rows is the least r >= 1 with m = 2, the exact least-row formula T_p(p^a+1) = p^(3a)+1.

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