Roger Fischer

Publication Date

1965

Document Type

Dissertation/Thesis

First Advisor

McKenzie, Harvey C.||Beach, James W.

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematics

LCSH

Fibonacci numbers; Number theory

Abstract

This paper treats the cycles formed by the residues of different Fibonacci series under prime modulis. I begin with a few elementary definitions and some background theorems which are assumed true. The basic relation under study is the comparison of lengths of different series and methods of predicting when cycles of shorter length than others of the same moduli occur. I first develop some foundational theorems true for all moduli and then consider two methods of determining short cycles. The first method, and its accompanying theorems, depends upon the use of exponential cycles under prime moduli. The bases for these cycles are solutions to the congruence a² ≡ a + 1 (mod p). The second method rests upon the concept of inverse cycles. These are defined and methods established for determining their existence. I conclude by showing the relationship between these two approaches and by summarizing the main topics of the paper.

Comments

Includes bibliographical references.

Extent

ii, 24 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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