---
id: 5900f3f31000cf542c50ff06
title: 'Problem 135: Same differences'
challengeType: 5
forumTopicId: 301763
dashedName: problem-135-same-differences
---

# --description--

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, x2 − y2 − z2 = n, has exactly two solutions is n = 27:

342 − 272 − 202 = 122 − 92 − 62 = 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?

# --hints--

`euler135()` should return 4989.

```js
assert.strictEqual(euler135(), 4989);
```

# --seed--

## --seed-contents--

```js
function euler135() {

  return true;
}

euler135();
```

# --solutions--

```js
// solution required
```