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blog/wilson-s-theorem-fermat-s-little-theorem-euler-s-totient-function/

Last time, we covered the Extended Euclidean Algorithm. Now, we’ll delve into some cooler number theory.
Wilson’s Theorem Wilson’s Theorem states that for any number $p$, the following congruence holds $\iff p$ is prime: $$(p-1)! \equiv -1 \pmod{p}$$ Proof Proof for composite numbers We can prove that this statement does not hold for any composite $p$ easily. Let $p$ be a composite number $\gt 2$. Then $p$ can be represented as the product of two numbers $a \cdot b = p$ for some $1 \leq a \leq b \lt p$.

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