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number of positive divisors is equal to n/5

Source: Azerbaijan NMO 2024. Senior P2

July 8, 2024
number theoryAZE SENIOR NATIONAL MO

Problem Statement

Let d(n)d(n) denote the number of positive divisors of the natural number nn. Find all the natural numbers nn such that d(n)=n5d(n) = \frac{n}{5}.
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