Primitive Triangles

 Published on Friday, 29th January 2010, 09:00 pm; Solved by 1027;
Difficulty rating: 75%

Problem 276

Consider the triangles with integer sides a, b and c with a ≤ b ≤ c.
An integer sided triangle (a,b,c) is called primitive if gcd(a,b,c)=1.
How many primitive integer sided triangles exist with a perimeter not exceeding 10 000 000?