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arXiv · 1711.04111

The Origin of the Beauregard--Suryanarayan Product on Pythagorean Triples

Shaul Zemel
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Abstract

We show how the multiplicative structure on Pythagorean triples defined by Beauregard--Suryanarayan arises from automorphisms of the hyperbolic plane, and how the structure theorem of this product follow naturally from this connection. We also show how the natural involution on Pythagorean triples is related to Pell's equation with the parameter 2, and prove a generalization of this phenomenon.

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Shaul Zemel. 2017-11-11. The Origin of the Beauregard--Suryanarayan Product on Pythagorean Triples. https://doi.org/10.1007/s11565-019-00319-0

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