I have the equation:
$A^x + B^y = C^z$
$A, B, C$ - constant value, $gcd(A, B) = 1$, $gcd(B, C) = 1$ and $gcd(A, C) = 1$.
$x, y, z \le 2^n$
$x, y, z \ge 3$
$A, B, C, x, y$, and $z$ are positive integers.
For specify the data $(A, B, C, n)$, there is no solution to the above equation?
Problem size is $n$.
Is it possible to prove that this problem is NP-complete?