I want an immediate solution.Can u help me in finding?

Question

Suppose
x^(n) = a^(m) - b^(m)
here n=/=m & a=/=b. n & m both should be greater then 2.
I want a solution to this equation where "a" & "b" are coprime ( i.e having no common factor between them) .
Can u help me out?

Answer 1

If n is contains an odd prime factor, this is part of an unsolved problem called Beal's conjecture. This says that if any
such solution exists, then a and b cannot be coprime.
If n is a power of 2, it is a multiple of 4, since n> 2.
A glance at Wikipedia also shows that this
case is also part of Beal's conjecture.
At the present time no counterexamples to
Beal's conjecture are known.
Incidentally, there is a $100000 prize for the
first proof or counterexample to Beal's conjecture.

Answer 2

Can't think of any clever approaches. If I had time I would start paddling around working out values of things like
5^3 - 2^3, 5^3 - 3^3, 8^5 - 7^5, but I'm already thinking it won't get anywhere useful. Sorry.