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Are there any patterns for formula for generating Pythagorean triplets?

Formula generating Mathematics patterns Pythagorean triplets
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Are there any patterns for formula for generating Pythagorean triplets?

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Euclid had the following formula: Given two positive integers, where m > n: a = m² – n² b = 2mn c = m² + n² For example, m = 2, n = 1: a = 2² – 1² = 3 b = 2(2)(1) = 4 c = 2² + 1² = 5 Or m = 3, n = 2: a = 3² – 2² = 5 b = 2(3)(2) = 12 c = 3² + 2² = 13

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