A tricky problem?

Question

Any number having any power (>1) can be expresed as difference of two coprime perfect squares.
from this show that for the equation
x^(m) = a^(n) - b^(n)
there exists no coprime solutions for x & b when "a" is given. Here m>2 & n>2.
Here m =/= n.

Answer 1

Right - This is ok in one particular problem, but not applicable for similar problems. How this formula can be utilized for our general mathematic (algebraic) problems is what I am searching for.