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Relationship n and its number of divisors

Source: Mexico National Olympiad 2014

November 13, 2014
inequalitiesinductionprobabilitynumber theory unsolvednumber theory

Problem Statement

Let d(n)d(n) be the number of positive divisors of a positive integer nn (including 11 and nn). Find all values of nn such that n+d(n)=d(n)2n + d(n) = d(n)^2.
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