Just an interesting side note, it is believed that Pythagoras stumbled onto this proof as he was climbing the stairs to his office and he looked down at the courtyard and in the mosaic tiles, he saw the pattern of three circles and a right angle triangle.
Poser: (3,4,5) is a Pythagorean triplet since 3^2 + 4^2 = 5^2. Which positive integers are not part of a Pythagorean triplet?
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