data/problems/136.yml
---
:id: 136
:name: Singleton difference
:url: https://projecteuler.net/problem=136
:content: |+
The positive integers, _x_, _y_, and _z_, are consecutive terms of an arithmetic progression. Given that _n_ is a positive integer, the equation, _x_<sup>2</sup> − _y_<sup>2</sup> − _z_<sup>2</sup> = _n_, has exactly one solution when _n_ = 20:
13<sup>2</sup> − 10<sup>2</sup> − 7<sup>2</sup> = 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?