Hi everybody,

Is there any proof that shows the following:

Ifpis prime, then each of the integers (lower to p) are relatively prime top. So for each of these integersathere is anotherbsuch thatab= 1 (modp). It is important to note that thisbis unique modulop.

I have encounter many times this conguence, however how is this comes up?

Also is there any similar congruence for integers bellow p^n?

Thank you all for your time.