## Singleton difference

### Problem 136

Published on Friday, 29th December 2006, 06:00 pm; Solved by 2726

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?