Fermat-like Equations
Problem 678
If a triple of positive integers satisfies , it is called a Pythagorean triple. No triple satisfies when (Fermat's Last Theorem). However, if the exponents of the left-hand side and right-hand side differ, this is not true. For example, .
Let be all positive integers, , , and . Let be the number of such that . You are given , and .
Find .