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n \leq 4m(2^m-1)-Iran 3rd round-Number Theory 2007

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July 28, 2010
number theory unsolvednumber theory

Problem Statement

Let m,nm,n be two positive integers and m≥2m \geq 2. We know that for every positive integer aa such that gcd⁡(a,n)=1\gcd(a,n)=1 we have n∣am−1n|a^m-1. Prove that n≤4m(2m−1)n \leq 4m(2^m-1).
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