dc.contributor.author | Scheibelhut, Kira | |
dc.date.accessioned | 2013-08-13T13:32:56Z | |
dc.date.available | 2013-08-13T13:32:56Z | |
dc.date.issued | 2013-08-13 | |
dc.identifier.uri | http://hdl.handle.net/10222/35316 | |
dc.description.abstract | An integer-valued polynomial is a polynomial with rational coefficients that takes an integer value when evaluated at an integer. The binomial polynomials form a regular basis for the Z-module of all integer-valued polynomials. Using the idea of a p-ordering and a p-sequence, Bhargava describes a similar characterization for polynomials that are integer-valued on some subset of the integers. This thesis focuses on characterizing the polynomials that are integer-valued on the Fibonacci numbers.
For a certain class of primes p, we give a formula for the p-sequence of the Fibonacci numbers and an algorithm for finding a p-ordering using Coelho and Parry’s results on the distribution of the Fibonacci numbers modulo powers of primes. Knowing the p-sequence, we can then find a p-local regular basis for the polynomials that are integer-valued on the Fibonacci numbers using Bhargava’s methods. A regular basis can be constructed from p-local bases for all primes p. | en_US |
dc.language.iso | en | en_US |
dc.subject | integer-valued polynomials | en_US |
dc.subject | Fibonacci numbers | en_US |
dc.subject | regular basis | en_US |
dc.subject | p-sequence | en_US |
dc.subject | p-ordering | en_US |
dc.title | Polynomials that are Integer-Valued on the Fibonacci Numbers | en_US |
dc.date.defence | 2013-08-06 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Master of Science | en_US |
dc.contributor.external-examiner | n/a | en_US |
dc.contributor.graduate-coordinator | Sara Faridi | en_US |
dc.contributor.thesis-reader | Karl Dilcher | en_US |
dc.contributor.thesis-reader | Dorette Pronk | en_US |
dc.contributor.thesis-supervisor | Keith Johnson | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Not Applicable | en_US |
dc.contributor.copyright-release | Not Applicable | en_US |