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Let T(N) be the number of distinct (non-congruent) triangles with integer sides and perimeter N. For example, T(12) = 3 because there are three distinct triangles with integer sides and perimeter 12. There’s the equilateral triangle with sides 4 : 4 : 4, and the Pythagorean triangle 3 : 4 : 5. With a little […] The post Counting triangles with integer sides first appeared on John D. Cook....