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There is no largest Pythagorean triple since there's infinite amount of them. But if you're looking for one quite big, I took a few minutes for you and wrote a program that computes them (and btw is still computing them). Right now the largest one the function returned is 77893200, 128189952, 150000048. Note that you can multiply all three with any same natural number larger than one (2,3,4,...) and you'll get a Pythagorean triple larger than mine.

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Q: What is the largest Pythagorean Triple?
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