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Definition of Sets

If p is pri...

Question

If $p$ is prime, show that $2 (p - 3)! + 1$ is a multiple of $p$ .

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Solution

According to Wilson's theorem if $p$ is a prime, then it would be divisible by $(p - 1)! + 1 = (p - 1) (p - 2) (p - 3)! + 1$
If $p - 1$ is divided by $p$ remainder is $- 1$
If $p - 2$ is divided by $p$ remainder is $- 2$
Hence, $p$ would be divisible by $- 1 \times - 2 \times (p - 3)! + 1 = 2 (p - 3)! + 1$

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