---
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, $x^2 − y^2 − z^2 = n$, has exactly one solution when $n = 20$:

$$13^2 − 10^2 − 7^2 = 20$$

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--

`singletonDifference()` should return `2544559`.

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

# --seed--

## --seed-contents--

```js
function singletonDifference() {

  return true;
}

singletonDifference();
```

# --solutions--

```js
// solution required
```