Problem 136
Singleton difference

The positive integers, x, y, and z, are consecutive terms of an arithmetic progression. Given that n is a positive integer, the equation, x2−y2−z2 = n, has exactly one solution when n = 20:

132− 102− 72 = 20

In fact there are twenty-five values of n below one hundred for which the equation has a unique solution.

How many values of n less than fifty million have exactly one solution?

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK