The origin of the Beauregard–Suryanarayan product on Pythagorean triples
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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.
KeywordsPythagorean triples Binary quadratic forms Pell’s equation
Mathematics Subject Classification11E16 11D57