Prouhet-Tarry-Escott problem

Named after Eugène Prouhet, who studied it in the early 1850s, and Gaston Tarry and Escott, who studied it in the early 1910s.

Prouhet-Tarry-Escott problem

1. (mathematics) The problem of finding two disjoint sets A and B of n integers each, such that ${\displaystyle \sum _{a\in A}a^{i}=\sum _{b\in B}b^{i}}$ for each integer i from 1 to a given k.