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Problem 370


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?