Prouhet–Tarry–Escott problem

In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint multisets A and B of n integers each, whose first k power sum symmetric polynomials are all equal. That is, the two multisets should satisfy the equations ∑ a ∈ A a i = ∑ b ∈ B b i {\displaystyle \sum _{a\in A}a^{i}=\sum _{b\in B}b^{i}} for each integer i from 1 to a given k.