Problem 292Published on Saturday, 15th May 2010, 01:00 am; Solved by 387; 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.