| viXra.org > Number Theory > viXra:2301.0080 |
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| viXra.org > Number Theory > viXra:2301.0080 |
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Number Theory |
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Authors: Filippo Giordano
The formula with which all the primitive Pythagorean triples are obtained, provided by Euclid around 300 BC, attributes to m, n alternative odd, even values, provided that m and n are coprime, i.e. without common divisors and that m> n. The same formula in cases where m, n, are both odd or both even provides only derived Pythagorean triples. After a specific search I found an alternative form to the algorithm which allows to obtain all the primitive Pythagorean triples a^2+b^2=c^2 by assigning both odd positive integer values to m, n and to obtain primitive Pythagorean triples but with mixed values (integers and decimals ) to a,b,c, assigning to m, n alternative odd, even values.
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[v1] 2023-01-17 02:21:45
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