---
id: 5900f5111000cf542c510023
title: 'Problem 420: 2x2 positive integer matrix'
challengeType: 5
forumTopicId: 302090
dashedName: problem-420-2x2-positive-integer-matrix
---

# --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).

# --hints--

`euler420()` should return 145159332.

```js
assert.strictEqual(euler420(), 145159332);
```

# --seed--

## --seed-contents--

```js
function euler420() {

  return true;
}

euler420();
```

# --solutions--

```js
// solution required
```