Number of Pythagorean Triples that Contain a Given Number

Author(s)	Aryan Phadke
Country	India
Abstract	Background: The study of the generation of Pythagorean triples is a topic that has been examined extensively in the past. One of the prominent formulae, which Euclid introduced in a parametric form, can produce all primitive Pythagorean triples by utilizing two integers. Problem Statement: To find a Pythagorean triple that includes a given number necessitates a distinct representation of the given number. Determining the number of potential Pythagorean triples becomes increasingly arduous since it mandates the expression of all factors of the given number in a specific format, which can be a laborious undertaking. Aim: The aim of this article is to create a set of constraints that generates the number of Pythagorean triples that contain a given number. Result: We have two constraint-based sets for when the given number is the hypotenuse and when it is a side other than the hypotenuse. It also will generate all Pythagorean triples with a parametric formula. It is apparent that this method is much simpler and more efficient to calculate the number of possible Pythagorean triples of a given number than Euclid's formula or other contemporary methods.
Keywords	Euclid’s formula, Pythagorean triples, Number of Pythagorean triples, Parametric formula
Field	Mathematics
Published In	Volume 5, Issue 5, September-October 2023
Published On	2023-10-09
DOI	https://doi.org/10.36948/ijfmr.2023.v05i05.7350

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