1. ## Wilson's theorem proof

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

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

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

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