Newton polygons and the Prouhet-Tarry-Escott problem (Q503726)

For \(n\geq 2\), the Prouhet-Tarry-Escott (PTE) problem asks for two lists of integers \(X=[x_1,\dots,x_n]\) and \(Y=[y_1,\dots,y_n]\) satisfying \(\sum_{i=1}^n x_i^e=\sum_{i=1}^n y_i^e\) for \(e\in\{1,\dots,k\}\), where \(k\) is an integer in the interval \([2,n-1]\). The authors use Newton polygons to obtain new information on the \(2\)-adic valuation of a certain constant associated with the PTE problem. Further, they give two explicit examples involving the cases \(n=8\) and \(n=9\).