---
id: 5900f4911000cf542c50ffa3
title: 'Problem 292: Pythagorean Polygons'
challengeType: 5
forumTopicId: 301944
dashedName: problem-292-pythagorean-polygons
---

# --description--

We shall define a pythagorean polygon to be a convex polygon with the following properties:

- there are at least three vertices,
- no three vertices are aligned,
- each vertex has integer coordinates,
- each edge has integer length.

For a given integer $n$, define $P(n)$ as the number of distinct pythagorean polygons for which the perimeter is $≤ n$.

Pythagorean polygons should be considered distinct as long as none is a translation of another.

You are given that $P(4) = 1$, $P(30) = 3655$ and $P(60) = 891045$.

Find $P(120)$.

# --hints--

`pythagoreanPolygons()` should return `3600060866`.

```js
assert.strictEqual(pythagoreanPolygons(), 3600060866);
```

# --seed--

## --seed-contents--

```js
function pythagoreanPolygons() {

  return true;
}

pythagoreanPolygons();
```

# --solutions--

```js
// solution required
```