Timothy Caley, Department of Pure Mathematics, University of Waterloo
"A new algorithm for the Prouhet-Tarry-Escott problem"
asks for integers x_1,..,x_n and y_1,...,y_n such that the sums of the
first k powers are equal. This problem has connections to combinatorics
and theoretical computer science, as well as to other areas of number
theory, such as Waring's problem.
The most interesting case is when k=n-1, which is called ideal. A major
open problem is determining whether ideal PTE solutions exist for a given
n, as well as characterizing those that do exist. Computational techniques
have been used to search for PTE solutions. In this talk, we present a new
algorithm to find PTE solutions, and explain how the results yield more
information than other computational searches in the literature.