dc.contributor.author Pechenick, Eitan dc.date.accessioned 2009-04-30 22:10:31 (GMT) dc.date.available 2009-04-30 22:10:31 (GMT) dc.date.issued 2009-04-30T22:10:31Z dc.date.submitted 2009 dc.identifier.uri http://hdl.handle.net/10012/4378 dc.description.abstract This thesis will survey a group of problems related to certain number-theoretic functions. In particular, for said functions, these problems take the form of when and how often they are equal over consecutive integers, n and n+1. The first chapter will introduce the functions and the histories of the related problems. The second chapter will take on a variant of the Ruth-Aaron pairs problem, which asks how often sums of primes of two consecutive integers are equal. The third chapter will examine, in depth, a proof by D.R. Heath-Brown of the infinitude of consecutive integer pairs with the same number of divisors---i.e. such that d(n)=d(n+1). After that we examine a similar proof of the infinitude of pairs with the same number of prime factors---ω(n)=ω(n+1). en dc.language.iso en en dc.publisher University of Waterloo en dc.subject number theory en dc.subject Ruth-Aaron pair en dc.subject divisors en dc.subject factors en dc.title Equality of Number-Theoretic Functions over Consecutive Integers en dc.type Master Thesis en dc.comment.hidden Third try's the charm? en Previous fixes: "Master of Mathematics" and Appendix lines in ToC. This version's fix: Added "Contents" heading for ToC. dc.pending false en dc.subject.program Pure Mathematics en uws-etd.degree.department Pure Mathematics en uws-etd.degree Master of Mathematics en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
﻿

### This item appears in the following Collection(s)

UWSpace

University of Waterloo Library
200 University Avenue West