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Problem 276

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Primitive Triangles

Consider the triangles with integer sides a, b and c with a ≤ b ≤ c.
An integer sided triangle (a,b,c) is called primitive if gcd(a,b,c)=1.
How many primitive integer sided triangles exist with a perimeter not exceeding 10 000 000?

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互质三角形

考虑三边长a ≤ b ≤ c均为整数的三角形。
如果gcd(a,b,c)=1，该整数边长三角形(a,b,c)就被称为互质三角形。
在边长不超过10 000 000的整数边长三角形中，存在多少个互质三角形？

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