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Prove that there exists a such that n | a^2 - a

Source: China TST 2011 - Quiz 3 - D1 - P2

May 20, 2011
modular arithmeticnumber theory proposednumber theory

Problem Statement

Let n>1n>1 be an integer, and let kk be the number of distinct prime divisors of nn. Prove that there exists an integer aa, 1<a<nk+11<a<\frac{n}{k}+1, such that n∣a2−an \mid a^2-a.
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