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Pythagorean Triples Almost everyone knows of the "3-4-5 triangle," one of the right triangles found in every draftsman's toolkit (along with the 45-45-90). This triangle is different from most right triangles because it has three integer edges. Pythagoras' theorem tells us that the squares of the sides of a right triangle sum to give to the square of the hypotenuse: 32 + 42 = 52 I am often asked whether this relationship is unique, or if there are other right triangles with three integer edges as well. When we randomly select two integers and add their squares, we usually acquire a non-integer square as a result; thus 32 + 52 = 34, or 42 + 72 = 65, and so on. Neither 34 nor 65 are integer squares. This type of result seems to be the general go of things; so the question posed is not without merit. It turns out that there are an...

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