Hi, first post here though I have been using the search feature to help myself through an onlin Intro to Number Theory class. I am stumped on two congruence questions.
1. If n>4 is a composite number, show that n|(n-1)! Conclude that (n-1)! not congruent -1(mod n).
(This shows that Wilson's theorem can be used as a proof of primality. It is unfortunately not practical for large numbers)
2. Use the congruence equation x^2 - 1 congruent 0(mod p) to show that if (a,p) = 1, then a^((p-1)/2) congruent +/- 1(mod p).
I in words why a composite (ab) number does not work, but am not really sure how to prove it. And for the second one, I do not really know how to start. Any help would be greatly appreciated as searching did not turn up anything really helpful to me.