The Pythagorean theorem, linking the sides of a right triangle, is one of the most useful basic mathematical identities. It is also one of the more entertaining. Loomis, in his book *The Pythagorean Proposition* (1968), gives 370 different proofs of the theorem. However, we’ll more often interested in computing the length of the hypotenuse, or finding triples—three natural numbers that makes the theorem hold—than finding a new proof for it.

There is, of course, the smallest possible triple (defined as involving the smallest possible numbers) 3, 4, 5. But there are infinitely more triples. Let’s see how we can generate them.

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