MathDB
Sum of exponents for all n

Source: Japan TST 2017 P3

January 24, 2021
number theory

Problem Statement

Find all positive integers kk such that there exist positive integer sequences a1,a2,…a_1,a_2,\ldots and r1,r2,…r_1,r_2,\ldots satisfying the following conditions:
[*] a1<a2<a3<…a_1<a_2<a_3<\ldots [*] a1k+a2k+…+ank=(a1+a2+…+an)rna_1^k+a_2^k+\ldots +a_n^k=(a_1+a_2+\ldots +a_n)^{r_n} holds for all positive integers nn.
Back to ProblemsView on AoPS