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?
The Attempt at a Solution
I'm thinking divinding the two might be pointless ..but subtracting might be a good idea.
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.