Problem 370Published on Sunday, 5th February 2012, 07:00 am; Solved by 324; Difficulty rating: 65%
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 ?