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## Homework Statement

Let c and d be two non-zero elements of a domain D. If a and b are integers s.t gcd(a,b)=1, a>0, b > 0.

If we know c^a=d^a and c^b=d^b,

does it follow that c=d?

## Homework Equations

## The Attempt at a Solution

I'm thinking divinding the two might be pointless ..but subtracting might be a good idea.

c^a-c^b=d^a-d^b.

Somehow have to use the fact that we are working in a domain? The hint is to consider the Quot(D) and work in it.