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CIIM 2010 Problem 5

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June 9, 2016
CIIMCIIM 2010undergraduate

Problem Statement

Let n,dn,d be integers with n,k>1n,k > 1 such that g.c.d(n,d!)=1g.c.d(n,d!) = 1. Prove that nn and n+dn+d are primes if and only if d!d((n−1)!+1)+n(d!−1)≡0( mod n(n+d)).d!d((n-1)!+1) + n(d!-1) \equiv 0 \hspace{0.2cm} (\bmod n(n+d)).
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