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sum of squares of divisors of k,n is n,k for all n

Source: IMOC 2018 N5

August 18, 2021
number theory

Problem Statement

Find all positive integers kk such that for every nāˆˆNn\in\mathbb N, if there are kk factors (not necessarily distinct) of nn so that the sum of their squares is nn, then there are kk factors (not necessarily distinct) of nn so that their sum is exactly nn.
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