Michael Mossinghoff

Affiliation: Center for Communications Research

Title Of Talk: Ideal solutions in the Prouhet-Tarry-Escott problem

Abstract: For given positive integers $m$ and $n$ with $m \lt n$, the \textit{Prouhet--Tarry--Escott problem} asks if there exist two disjoint multisets of integers of size $n$ having identical $k$th moments for $1\leq k\leq m$; in the \textit{ideal} case one requires $m=n-1$, which is maximal. We describe some new searches for ideal solutions to the Prouhet--Tarry--Escott problem, especially solutions possessing a particular symmetry, both over $\mathbb{Z}$ and over the ring of integers of several imaginary quadratic number fields. This is joint work with D. Coppersmith, D. Scheinerman, and J. VanderKam.

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