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Pythagorean Triples

Pythagorean triples are sets of three integers that are solutions to the associated identity for right triangles.

The question is this:

Can you find a formula or algorithm for generating Pythagorean Triples?

There may be more than one formula, and each might not be exhaustive. All we are after is a set of rules such that, given one number, can you find the other two that belong to the triplet?

pythagorean theorem