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p divides sigma(p-1)

Source: Oliforum math contest, problem 1

September 30, 2009
functionmodular arithmeticnumber theoryprime factorizationnumber theory proposed

Problem Statement

Let σ(⋅):N0→N0 \sigma(\cdot): \mathbb{N}_0 \to \mathbb{N}_0 be the function from every positive integer n n to the sum of divisors ∑d∣nd \sum_{d \mid n}{d} (i.e. \sigma(6) \equal{} 6 \plus{} 3 \plus{} 2 \plus{} 1 and \sigma(8) \equal{} 8 \plus{} 4 \plus{} 2 \plus{} 1). Find all primes p p such that p \mid \sigma(p \minus{} 1). (Salvatore Tringali)
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