Modulus of a large prime, a smaller prime multiplied by a positive factor n doesn't repeat.

Modulus of a large prime, a smaller prime multiplied by a positive factor
n doesn't repeat.

Given a prime p1 and a prime p2 (where p2 < p1), I made the observation
that with a number n (where n increases by 1 from the value 1) the
equation below results in two properties:
x = (p2 * n) mod p1
The first repeat is the value p2 where n = p1 + 1.
Somewhat as a function of the first property all the values in the range
0..p1 are consumed before reaching that repeat.
I've tested this property on paper with small primes and with some large
primes by writing some code to confirm these properties, but does anyone
know why this property holds?