Question

Prove that an integer $p>2$ is prime if and only if $(p-2)!\bmod p=1$.

   Prove that an integer $p>2$ is prime if and only if $(p-2)!\bmod p=1$.

Applied Algebra: Codes, Ciphers and Discrete Algorithms

Applied Algebra: Codes, Ciphers and Discrete Algorithms

Darel W. Hardy, Fred… 2nd Edition

Chapter 7, Problem 8

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Step 1

We need to prove that an integer \( p > 2 \) is prime if and only if \( (p-2)! \equiv 1 \pmod{p} \). Recall that a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Show more…

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Prove that an integer $p>2$ is prime if and only if $(p-2)!\bmod p=1$.

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