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Problem 8 - Entrance Test

Let p be a prime. How many primes p ≤ 50 satisfy p divides (p−1)!+1?

Correct: A

By Wilson’s theorem, (p−1)!≡−1 (mod p) for all primes p. Thus (p−1)!+1≡0 (mod p) for every prime. There are 15 primes ≤ 50.