The origin of the Beauregard–Suryanarayan product on Pythagorean triples

  • Shaul ZemelEmail author


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.


Pythagorean triples Binary quadratic forms Pell’s equation 

Mathematics Subject Classification

11E16 11D57 



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Copyright information

© Università degli Studi di Ferrara 2019

Authors and Affiliations

  1. 1.Einstein Institute of MathematicsThe Hebrew University of Jerusalem, Edmond Safra CampusJerusalemIsrael

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