Wilson's theorem
Theorem on prime numbers / From Wikipedia, the free encyclopedia
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In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n. That is (using the notations of modular arithmetic), the factorial satisfies
exactly when n is a prime number. In other words, any integer n > 1 is a prime number if, and only if, (n − 1)! + 1 is divisible by n.[1]