Ideal solutions in the Prouhet-Tarry-Escott problem (Michael Mossinghoff, Center for Communications Research, Princeton)

For given positive integers m and n with m<n, the 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 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 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.