Number Theory


Number of Pythagorean Triples and Expansion of Euclid's Formula

Authors: Aryan Phadke

Set of Pythagorean triple consists of three values such that they comprise the three sides of a right angled triangle. Euclid gave a formula to find Pythagorean Triples for any given number. Motive of this paper is to find number of possible Pythagorean Triples for a given number. I have been able to provide a different proof for Euclid’s formula, as well as find the number of triples for any given number. Euclid’s formula is altered a little and is expanded with a variable ‘x’. When ‘x’ follows the conditions mentioned the result is always a Pythagorean Triple.

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[v1] 2019-05-30 02:35:37

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