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Euler's totient function and sum of divisor function

Source: 11th CHKMO 2009

December 15, 2008
functionEuleralgebrapolynomialVietaquadraticsnumber theory

Problem Statement

Let n>4 n>4 be a positive integer such that n n is composite (not a prime) and divides \varphi (n) \sigma (n) \plus{}1, where φ(n) \varphi (n) is the Euler's totient function of n n and σ(n) \sigma (n) is the sum of the positive divisors of n n. Prove that n n has at least three distinct prime factors.
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