{"id":"hexagon/2611.00057","pdf":"https://hexagonmath.org/pdf/2611.00057v1","url":"https://hexagonmath.org/abs/2611.00057v1","tags":["msc:11D72","msc:11S05","msc:11P05","$2$-adic valuation","Newton polygons","Prouhet-Tarry-Escott problem","ideal solutions","multigrades","symmetric solutions"],"score":0,"title":"The 2-adic valuation of the constant for symmetric ideal Prouhet-Tarry-Escott solutions","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 $n$, let $C$ denote the associated constant, and let $\\overline{C_n}$ be the greatest common divisor of these constants. Filaseta and Markovich obtained $v_2(\\overline{C_8})\\ge6$ and determined $v_2(\\overline{C_9})=9$, and asked for improved lower bounds in the range $10\\le n\\le12$; Bera and Nair gave bounds for $n=10$ and $n=12$. We treat the symmetric case at every size, even and odd, by $2$-adic arguments throughout. A single identity, the row law, governs both parities. For $n$ even, over $\\mathbb{Z}$, it splits into two…","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Opus"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}