On the Largest Integer that is not a Sum of Distinct Positive nth Powers

摘要

It is known that for an arbitrary positive integer n the sequence S(xn) = (1n, 2n, ...) is complete, meaning that every sufficiently large integer is a sum of distinct nth powers of positive integers. We prove that every integer         m ≥ (b - 1)2n-1(r + (2/3)(b - 1)(22n - 1) + 2(b - 2))n - 2a + ab, where a = n!2n2, b= 2n3an-1, r = 2n2 - na, is a sum of distinct positive nth powers.