The origin of the Beauregard–Suryanarayan product on Pythagorean triples

Shaul Zemel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageAmerican English
Pages (from-to)389-409
Number of pages21
JournalAnnali dell'Universita di Ferrara
Issue number2
StatePublished - 1 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019, Università degli Studi di Ferrara.


  • Binary quadratic forms
  • Pell’s equation
  • Pythagorean triples


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