1. The problem statement, all variables and given/known data
Suppose [d], [tex]\in[/tex] Z sub n.
The good news here is, that you can perform all operations in Zm by picking any representative and working in the integers.
So if c sits in the conjugacy class of a, you can write
c = a + i m
where 0 <= a < m and i is some integer, similarly
d = b + j m
If cd is congruent to ab mod m, then cd lies in [ab] by definition, doesn't it?
If you want a less trivial proof, show that
cd = ab + km
for some integer k.
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