Lethbridge Number Theory and Combinatorics Seminar: Renate Scheidler

It is well-known that the continued fraction expansion of a quadratic irrational is horizontally symmetric about its centre.
However, an additional vertical symmetry is exhibited by the continued fraction expansions arising from a certain one-parameter family of positive integers known as Schinzel sleepers. This talk provides a method for generating any Schinzel sleeper and investigates their period lengths as well as both their horizontal and vertical symmetries.

This is joint work with Kell Cheng (Hongkong Institute of Education) as well as Richard Guy and Hugh Williams (University of Calgary). The talk is geared toward an audience with a background corresponding to no more than a first number theory course.