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. `b ^{2}` =

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 10^{6} .

How many geometric triangles exist with perimeter 2.5·10^{13} ?

**
These problems are part of
Project Euler
and are licensed under
CC BY-NC-SA 2.0 UK
**