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Easy number theory 2017 Taiwan TST

Source: 2017 Taiwan TST Round 1

April 13, 2018
number theory

Problem Statement

For postive integers k,nk,n, let fk(n)=∑m∣n,m>0mkf_k(n)=\sum_{m\mid n,m>0}m^k Find all pairs of positive integer (a,b)(a,b) such that fa(n)∣fb(n)f_a(n)\mid f_b(n) for every positive integer nn.
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