Prouhet-Tarry-Escott problem

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

Proper noun

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