Is there any proof that shows the following:
If p is prime, then each of the integers (lower to p) are relatively prime to p. So for each of these integers a there is another b such that ab = 1 (mod p). It is important to note that this b is unique modulo p.
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.