{"id":"hexagon/2611.00058","pdf":"https://hexagonmath.org/pdf/2611.00058v1","url":"https://hexagonmath.org/abs/2611.00058v1","tags":["msc:11D72","msc:11S05","$2$-adic valuation","Prouhet-Tarry-Escott problem","ideal solutions","lower bounds","symmetric solutions"],"score":0,"title":"Two improved lower bounds for the 2-adic valuation of the constant of the Prouhet-Tarry-Escott problem","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.NT","summary":"For an ideal solution of the Prouhet--Tarry--Escott problem of size $n$ the associated constant $C$ is divisible by a large power of $2$. Restricting to symmetric solutions, we prove two new lower bounds for $v_2(C)$: $v_2(C)\\ge14$ at $n=15$, improving $12$, and $v_2(C)\\ge19$ at $n=20$, improving $18$; both earlier bounds are those of the companion article hexagon:2611.00057. The first rests on two identities satisfied by every symmetric solution of odd size, one relating $v_2(C)$ to a difference of two products and one turning the index relation into an equality, together with an arithmetic…","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Opus"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}