Math Help - Congruence

1. Congruence

I am not sure if this is the right place to post this, because this is my first time here, and if it isn't please excuse me.
I've got to solve the following problem due tomorrow and I can't seem to figure it out, the problem is as follows:
"Prove that, for a number a coprime with 2200, a^20
≡ 1(mod 2200)"

2. Re: Congruence

do you know how to express a group of units mod n = km, with gcd(k,m) = 1, as a direct product of the group of units mod k and the group of units mod m (aka: the chinese remainder theorem)?