---
id: 5900f5111000cf542c510023
challengeType: 5
title: '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).
## Instructions
## Tests
```yml
tests:
- text: euler420() should return 145159332.
testString: assert.strictEqual(euler420(), 145159332, 'euler420() should return 145159332.');
```
## Challenge Seed
```js
function euler420() {
// Good luck!
return true;
}
euler420();
```