On the compatibility of Bézout coefficients between Pythagorean pairs under unimodular transformations

Abstract

In a recent preprint, Gullerud and Walker [2] proved a theorem and made a conjecture about the correctness of efficiently generating Bézout trees for Pythagorean pairs. In this note, we give a simple proof of their theorem, confirm that their conjecture is true, and furthermore we give a generalization.