Problem 370
Geometric triangles
Let us define a geometric triangle as an integer sided triangle with sides a 
b c so that its sides form a geometric progression, i.e. b2 = a · c .
An example of such a geometric triangle is the triangle with sides a = 144, b = 156 and c = 169.
There are 861805 geometric triangles with perimeter 106 .
How many geometric triangles exist with perimeter 2.5·1013 ?
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK