COMMENTS

The multisets of zeros of two degree-n polynomials with an integer difference form an ideal solution to the Prouhet-Tarry-Escott problem of size n. Correspondingly, a(n) equals the smallest difference between the products of multisets terms in an ideal solution. By the Newton-Girard formulas, the same ideal solutions deliver the smallest difference between the sums of n-th powers (cf. A296137).