---
id: 5900f3f51000cf542c50ff07
challengeType: 5
title: 'Problem 136: Singleton difference'
forumTopicId: 301764
---
## Description
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?
## Instructions
## Tests
```yml
tests:
- text: euler136() should return 2544559.
testString: assert.strictEqual(euler136(), 2544559);
```
## Challenge Seed
```js
function euler136() {
// Good luck!
return true;
}
euler136();
```