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Geometric triangles

Problem 370

Published on Sunday, 5th February 2012, 07:00 am; Solved by 343

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 ?