Show simple item record

dc.contributor.advisorMbirika, aBa
dc.contributor.authorFiebig, Morgan
dc.date.accessioned2025-01-29T19:06:34Z
dc.date.available2025-01-29T19:06:34Z
dc.date.issued2024-04
dc.identifier.urihttp://digital.library.wisc.edu/1793/94442
dc.descriptionColor poster with text, charts, and diagrams.en_US
dc.description.abstractThe Pisano periods and entry points in the Fibonacci sequence has been a well-studied subject since D.D. Wall’s seminal paper in 1960. The Pisano period is the length of consecutive sequence terms which repeat infinitely to comprise the entire sequence modulo m, the entry point is the index at which the first zero appears in the sequence modulo m, and the order of m is the ratio of the Pisano period to the entry point. We have extended this study to other well known second-order linear recurrence sequences modulo m: Lucas, Pell, associated Pell, balancing, Lucas-balancing, cobalancing, and Lucas-cobalancing. Using data collected through programming in Mathematica, we have observed that the order of m can be used to predict many interesting patterns in the sequence terms modulo m. In particular, we observe that cyclic group structures, palindromes, and semi-palindromic behaviors can all be predicted based on the order of m, and that the m values for which the order of m is four form multiplicative monoids in some settings.en_US
dc.description.sponsorshipUniversity of Wisconsin--Eau Claire Office of Research and Sponsored Programsen_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesUSGZE AS589;
dc.subjectFibonacci sequenceen_US
dc.subjectModulusen_US
dc.subjectNumber theoryen_US
dc.subjectPostersen_US
dc.subjectDepartment of Mathematicsen_US
dc.titlePatterns in the Pisano Period and Entry Points of Linear Recurrence Sequences Modulo Men_US
dc.typePresentationen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

  • CERCA
    Posters of collaborative student/faculty research presented at CERCA

Show simple item record