Prouhet's problem | Tarry-Escott problem

Find two distinct sets of integers {a_1, ..., a_n} and {b_1, ..., b_n}, such that for k = 1, ..., m, sum_(i = 1)^n (a_i)^k = sum_(i = 1)^n (b_i)^k. The Prouhet-Tarry-Escott problem is therefore a special case of a multigrade equation. Solutions with n = m + 1 are said to be "ideal" and are of interest because they are minimal solutions of the problem.