aBa Mbirika, University of Wisconsin-Eau Claire
Authors: aBa Mbirika, Janee Schrader, and J"urgen Spilker
2023 AWM Research Symposium
Number Theory at Primarily Undergraduate Institutions [Organized by Bella Tobin and Leah Sturman]

This talk will focus on the research projects conducted with my undergraduate students on numerical sequences. My introduction to research in this area began in June 2018, when I stumbled on a YouTube video by a famous astrologer, named David Cochrane, and he made some number theoretic connections between the Fibonacci sequence and astrology. Cochrane is no mathematician, but his video presented a number of conjectures, all of a mathematical nature, which immediately became a source of research for my students that year. That work has been published, and each year since then, my new undergraduate students and I completed research projects on various numerical sequences, leading to publications as well as fond memories. A prominent part of this talk focuses on the most recent publication, which is a joint work with my research student Janee Schrader and my external collaborator Dr.~Jurgen Spilker in Germany. We consider six different linear recurrence sequences: Pell $P_n$, associated Pell $Q_n$, balancing $B_n$, Lucas-balancing $C_n$, cobalancing $b_n$, and Lucas-cobalancing $c_n$ numbers. We compute a closed form for the greatest common divisor of all sums of $k$ consecutive numbers coming from each of these six sequences. This talk should be accessible to a wide audience. I also promise that the word ``tantalizing'' was very intentionally placed in the talk title; these projects will excite your senses and may lead you to do your own explorations of these fascinating sequences!

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