data/problems/135.yml
---
:id: 135
:name: Same differences
:url: https://projecteuler.net/problem=135
:content: |+
Given the positive integers, _x_, _y_, and _z_, are consecutive terms of an arithmetic progression, the least value of the positive integer, _n_, for which the equation, _x_<sup>2</sup> − _y_<sup>2</sup> − _z_<sup>2</sup> = _n_, has exactly two solutions is _n_ = 27:
34<sup>2</sup> − 27<sup>2</sup> − 20<sup>2</sup> = 12<sup>2</sup> − 9<sup>2</sup> − 6<sup>2</sup> = 27
It turns out that _n_ = 1155 is the least value which has exactly ten solutions.
How many values of _n_ less than one million have exactly ten distinct solutions?