Talk:Reduced residue system

Fact 2

In the facts section fact #2 was incorrect. It was saying

• If n is prime, then every number in a reduced residue system mod n (except for 1) is a generator for the multiplicative group of integers mod n.

Consider e.g. n=5. Then {-2,-1,1,2} is a reduced residue system, but $(-1)\cdot (-1)=1$, so (-1) doesn't generate the multiplicative group. I will remove it and replace with the following.

• Every number in a reduced residue system mod n is a generator for the additive group of integers modulo n.

That's true, because if gcd(r, n) = 1, then ra+nb=1 for some integers a,b and therefore $ra\equiv 1{\pmod {n}}$. Thus 1 modulo n can be obtained by adding r to itself mod(a,n) times. Vikasatkin (talk) 17:09, 14 October 2014 (UTC)