{"id":"hexagon/2611.00076","pdf":"https://hexagonmath.org/pdf/2611.00076v1","url":"https://hexagonmath.org/abs/2611.00076v1","tags":["msc:11T55","msc:11A07","msc:11T06","Carlitz factorial","Hasse derivatives","Wilson primes","function fields","polynomials over finite fields","supercongruences"],"score":0,"title":"The exact multiplicity of the Wilson supercongruence in F_q[t]","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.NT","summary":"Let q = p^s with p an odd prime, and let P be a monic irreducible polynomial of degree d >= 2 in F_q[t]. The Wilson analogue F_d = -1 mod P holds for the product F_d of all nonzero polynomials of degree less than d, and Thakur proved that P is a Wilson prime, i.e. F_d = -1 mod P^2, exactly when all exponents of P are congruent to 0 or 1 mod p, in which case the congruence holds modulo P^(p-1). He asked whether it can hold modulo a higher power, and what the exact multiplicities are. Let r be the largest integer such that all exponents of P are congruent to 0 or 1 modulo p^r. We prove that…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}