Let be a reduced residue system modulo m (n = ф(m)).

Show that the numbers form a reduced residue system

(mod m) if and only if (k, ф(m)) = 1.

I am thinking of letting g be a primitive root modulo m, so that will be a reduced residue system. Then, somehow, will be a reduced residue system if (k, ф(m)) = 1.

Could anyone help me prove this? Thanks.