Modular Schur numbers: S_m(k,ℓ) = n − 1 for k ≥ n − 1, where n = m/gcd(m,ℓ−1)
A Lean 4 formalization, with Mathlib, of the main results of the paper "Prime-power structure of the stable regime for modular Schur numbers" (docs/paper/modular-schur.pdf in this repository). The modular Schur number S_m(k,ℓ), introduced by Chappelon, Revuelta Marchena and Sanz Domínguez (2013), is the largest N such that 1, …, N can be coloured with k colours so that no colour class contains a solution of x_1 + ⋯ + x_ℓ ≡ y (mod m). For m ≥ 2 and ℓ ≥ 2, put n = m/gcd(m,ℓ−1). The main theorem is the closed form S_m(k,ℓ) = n − 1 for every k ≥ n − 1. D'orville, Sim, Wong and Ho (Integers 25…
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