## Pythagorean Polygons

### Problem 292

Published on Saturday, 15th May 2010, 01:00 am; Solved by 407; Difficulty rating: 65%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).