---
id: 5900f3f51000cf542c50ff07
title: 'Problem 136: Singleton difference'
challengeType: 5
forumTopicId: 301764
dashedName: problem-136-singleton-difference
---

# --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?

# --hints--

`euler136()` should return 2544559.

```js
assert.strictEqual(euler136(), 2544559);
```

# --seed--

## --seed-contents--

```js
function euler136() {

  return true;
}

euler136();
```

# --solutions--

```js
// solution required
```
