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\phi (n)+1 (not necessarily different) divisors n with the sum n

Source: 2021 Ukraine NMO 10.8 11.7

April 4, 2021
number theoryDivisors

Problem Statement

Given a natural number nn. Prove that you can choose ϕ(n)+1 \phi (n)+1 (not necessarily different) divisors nn with the sum nn.
Here ϕ(n) \phi (n) denotes the number of natural numbers less than nn that are coprime with nn.
(Fedir Yudin)
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