# Talk:Reduced residue system

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Field:  Number theory

## Fact 2

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

Consider e.g. n=5. Then {-2,-1,1,2} is a reduced residue system, but ${\displaystyle (-1)\cdot (-1)=1}$, 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 ${\displaystyle ra\equiv 1{\pmod {n}}}$. Thus 1 modulo n can be obtained by adding r to itself mod(a,n) times. Vikasatkin (talk) 17:09, 14 October 2014 (UTC)