Lethbridge Number Theory and Combinatorics Seminar: John Voight

Given coprime integers $a,b$, the classical identity of Bezout provides integers $u,v$ such that $au-bv = 1$. We consider refinements to this identity, where we ask that $u,v$ are norms from a quadratic extension. We then find ourselves counting optimal embeddings of a quadratic order in a quaternion order, for which we give explicit formulas in many cases. This is joint work with Donald Cartwright and Xavier Roulleau.