1) Show that (mod p) when p is an odd prime

2) Show that ifpis a prime andp> 3, then (mod p)

For 1), I really don't understand which theorem or identity I'm supposed to put into use to prove this. Obviously it works every time I just don't understand how this works in terms of technicality.

2) is the same story. I don't see how it works and therefore I can't prove it formally.