The 2-adic valuation of the constant for symmetric ideal Prouhet-Tarry-Escott solutions
Source: hexagonmath.org/abs/2611.00057v1
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…
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