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dc.contributor.authorPechenick, Eitan 22:10:31 (GMT) 22:10:31 (GMT)
dc.description.abstractThis 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.publisherUniversity of Waterlooen
dc.subjectnumber theoryen
dc.subjectRuth-Aaron pairen
dc.titleEquality of Number-Theoretic Functions over Consecutive Integersen
dc.typeMaster Thesisen
dc.comment.hiddenThird try's the charm? Previous fixes: "Master of Mathematics" and Appendix lines in ToC. This version's fix: Added "Contents" heading for ToC.en
dc.subject.programPure Mathematicsen Mathematicsen
uws-etd.degreeMaster of Mathematicsen

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