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(n-2)!=an+1 iff n prime

Source: Yugoslav TST 1968 P2

May 29, 2021
number theory

Problem Statement

Let n>3n>3 be a positive integer. Prove that nn is prime if and only if there exists a positive integer α\alpha such that n!=n(n−1)(αn+1)n!=n(n-1)(\alpha n+1).
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