freeCodeCamp/curriculum/challenges/en/08-coding-interview-prep/project-euler/problem-420-2x2-positive-integer-matrix.en.md

---
id: 5900f5111000cf542c510023
challengeType: 5
title: 'Problem 420: 2x2 positive integer matrix'
---

## Description
<section id='description'>
A positive integer matrix is a matrix whose elements are all positive integers.
Some positive integer matrices can be expressed as a square of a positive integer matrix in two different ways. Here is an example:





We define F(N) as the number of the 2x2 positive integer matrices which have a trace less than N and which can be expressed as a square of a positive integer matrix in two different ways.
We can verify that F(50) = 7 and F(1000) = 1019.



Find F(107).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
- text: <code>euler420()</code> should return 145159332.
  testString: 'assert.strictEqual(euler420(), 145159332, ''<code>euler420()</code> should return 145159332.'');'

```

</section>

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

<div id='js-seed'>

```js
function euler420() {
  // Good luck!
  return true;
}

euler420();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>