Date of Publication

8-27-2011

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Leonor Aquino-Ruivivar

Defense Panel Chair

Yvette Fajardo-Lim

Defense Panel Member

Melvin A. Vidar
Sonia Y. Tan

Abstract/Summary

Define the set of generalized Carmichael numbers, Ck, to be the set containing

natural numbers n such that an+k _ a (mod n) for all natural numbers n.

We consider the set Ck for certain integer values of k and identify the form of

some of its elements. In particular, we show that the set Ck contains finitely

many elements with exactly two prime factors whenever 1 �� k > 1 is squarefree.

Also, we investigate a more specific type of Carmichael numbers, called

generalized Jeans numbers, where the congruence given above holds for a given

value of a only. A generalized Jean number is defined to be a natural number

n such that bn+k _ b (mod n) for a fixed natural number b. We provide a

necessary and sufficient condition for a natural number to be a generalized

Jeans number and identify the form of some of these numbers.

Abstract Format

html

Language

English

Format

Electronic

Electronic File Format

MS WORD

Accession Number

CDTG004996

Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

56 leaves : ill. :; 28 cm.

Keywords

Numbers, Natural; Factor tables

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2-7-2022

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