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Number of Divisors in the Exponent

Source: 2012 Baltic Way, Problem 17

November 22, 2012
number theory unsolvednumber theory

Problem Statement

Let d(n)d(n) denote the number of positive divisors of nn. Find all triples (n,k,p)(n,k,p), where nn and kk are positive integers and pp is a prime number, such that nd(n)āˆ’1=pk.n^{d(n)} - 1 = p^k.
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