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University of Illinois at Urbana-Champaign

Topics in Combinatorial Number Theory

Abstract

dc:description

In this dissertation we present a number of new results in combinatorial number theory. Chapter I discusses a generalization of B(,2)-sequences which are used in Chapter II and Chapter III to obtain short interval results about k-free values of irreducible polynomials. Chapter IV deals with the number of partitions of an integer using a set of distinct parts; Chapter V demonstrates how a single prime value of a polynomial with non-negative coefficients can be used to show that the polynomial is irreducible; Chapter VI compares simple continued fraction convergents for SQRT.(N) with Newton approximations to SQRT.(N); and Chapter VII obtains exact formulas for a certain class of ballot problems. An introduction is included which gives preliminary discussions on various aspects of the problems.

Degree

thesis:*
Name thesis:degree_name
Ph.D.
Level thesis:degree_level
Dissertation
Discipline thesis:degree_discipline
Mathematics
Grantor
University of Illinois at Urbana-Champaign
Year dc:date
2014

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Filaseta, Michael Anthony

Subjects

dc:subject × 1

Identifiers

dc:identifier.*
Identifier
(UMI)AAI8502140
OAI identifier oai:identifier
oai:www.ideals.illinois.edu:2142/71225

Chain of custody

source
Harvested from
University of Illinois - Urbana-Champaign
Base URL
www.ideals.illinois.edu/oai-pmh
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
citation

Filaseta, Michael Anthony. Topics in Combinatorial Number Theory. Dissertation thesis, University of Illinois at Urbana-Champaign, 2014. http://hdl.handle.net/2142/71225