# Thread: Distinct residue modulo

1. ## Distinct residue modulo

Hi

Can someone kindly explain to me why in the sequence, they are all distinct?
a mod p, a^2 mod p, a^3 mod ... are all distinct?

If so, how do we know which element in the afrmentioned sequence is equal to the element in the sequence below:
1 mod p, 2 mod p, ..., (p-1) mod p.

Thanks.

2. Well they are not all distinct. Obviously there are at most $p-1$ possible values.

It may happen that $a, ..., a^{p-1}$ are all distinct. In this case we say $a$ is a primitive root mod $p$. Generally though $a$ is not a primitive root.