Number Theory

[Ari]

Can anyone help me with this? Show that if a, b, and c are positive integers with gcd(a, b) = 1 and ab = c^n, then there are positive integers d, and e such that a = d^n and b = e^n.
Thanks!

 

[tkhunny]

We can get started by working on the exponents being required to be equal.

What is the case if they are not? Take m = n+1 and see how it goes for a = d^n and b = e^m.