Wilson's theorem proof

**Ben92** · July 15th 2009, 06:45 AM

Hello!

My question is simple: What do you think my own Wilson's theorem proof? http://benmartin.winportal.net/wilson.pdf Is that mathematically correct or isn't it?

Thank you

Ben

**PaulRS** · July 16th 2009, 05:48 AM

Why is $p^{\epsilon}\cdot x \equiv{(n-1)!} (\bmod.n)$ true ?

If you had proved that, it'd been correct, but you see, you chose a number $p$ and said that $p^{\epsilon}\cdot x \equiv{n-1} (\bmod.n)$ is solvable, but that tells you nothing about $(n-1)!$ .

Having $\epsilon_{p}(n)<n-1$ doesn't influence the fact that the congruence $p^{\epsilon}\cdot x \equiv{(n-1)} (\bmod.n)$ has solutions if $(p,n)=1$ .

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