---
id: 5900f4521000cf542c50ff64
challengeType: 5
title: 'Problem 229: Four Representations using Squares'
forumTopicId: 301872
---

## Description
<section id='description'>
Consider the number 3600. It is very special, because

3600 = 482 +     362
3600 = 202 + 2×402
3600 = 302 + 3×302
3600 = 452 + 7×152

Similarly, we find that 88201 = 992 + 2802 = 2872 + 2×542 = 2832 + 3×522 = 1972 + 7×842.

In 1747, Euler proved which numbers are representable as a sum of two squares.
We are interested in the numbers n which admit representations of all of the following four types:

n = a12 +   b12n = a22 + 2 b22n = a32 + 3 b32n = a72 + 7 b72,

where the ak and bk are positive integers.

There are 75373 such numbers that do not exceed 107.

How many such numbers are there that do not exceed 2×109?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler229()</code> should return 11325263.
    testString: assert.strictEqual(euler229(), 11325263);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler229() {
  // Good luck!
  return true;
}

euler229();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>