AIMS Mathematics, 2019, 4(2): 242-253. doi: 10.3934/math.2019.2.242.

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A new approach to generate all Pythagorean triples

1 Department of Information Technology, Melbourne Polytechnic, VIC, Australia
2 Department of Mathematics and Statistics, Curtin University, Perth (WA), Australia

This paper revisits the topic of Pythagorean triples with a different perspective. While several methods have been explored to generate Pythagorean triples, none of them is complete in terms of generating all the triples without repetitions. Indeed, many existing methods concentrate on generating primitive triples but do not cater to non-primitives. By contrast, the approach presented in this paper to parameterise the Pythagorean triples generates all of the triples in a unique way, i.e., without repetitions. We also explore the relation of this new parameterisation with the Pythagorean family of odd triples and with the Platonic family of even triples.
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Keywords Pythagorean triples; Diophantine equations; Euclidean triples; Platonic triples; right angle triangles

Citation: Anthony Overmars, Lorenzo Ntogramatzidis, Sitalakshmi Venkatraman. A new approach to generate all Pythagorean triples. AIMS Mathematics, 2019, 4(2): 242-253. doi: 10.3934/math.2019.2.242


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