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 ?
等比三角形
若三角形的边长为整数a ≤ b ≤ c，且构成等比数列，即b2 = a · c ，则称之为等比三角形。
一个等比三角形的例子是边长为a = 144、b = 156、c = 169的三角形。
周长≤ 106的等比三角形有861805个。
周长≤ 2.5·1013的等比三角形有多少个？