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Now showing items 1-9 of 9

    • Computational Methods for Combinatorial and Number Theoretic Problems 

      Bright, Curtis (University of Waterloo, 2017-04-27)
      Computational methods have become a valuable tool for studying mathematical problems and for constructing large combinatorial objects. In fact, it is often not possible to find large combinatorial objects using human ...
    • Equality of Number-Theoretic Functions over Consecutive Integers 

      Pechenick, Eitan (University of Waterloo, 2009-04-30)
      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 ...
    • Generalisations of Roth's theorem on finite abelian groups 

      Naymie, Cassandra (University of Waterloo, 2012-12-18)
      Roth's theorem, proved by Roth in 1953, states that when A is a subset of the integers [1,N] with A dense enough, A has a three term arithmetic progression (3-AP). Since then the bound originally given by Roth has been ...
    • Multiplicities of Linear Recurrence Sequences 

      Allen, Patrick (University of Waterloo, 2006)
      In this report we give an overview of some of the major results concerning the multiplicities of linear recurrence sequences. We first investigate binary recurrence sequences where we exhibit a result due to Beukers and ...
    • On a Question of Wintner Concerning the Sequence of Integers Composed of Primes from a Given Set 

      Kim, Jeongsoo (University of Waterloo, 2007-09-27)
      We answer to a Wintner's question concerning the sequence of integers composed of primes from a given set. The results generalize and develop the answer to Wintner’s question due to Tijdeman.
    • On Transcendence of Irrationals with Non-eventually Periodic b-adic Expansions 

      Koltunova, Veronika (University of Waterloo, 2010-05-18)
      It is known that almost all numbers are transcendental in the sense of Lebesgue measure. However there is no simple rule to separate transcendental numbers from algebraic numbers. Today research in this direction is about ...
    • The Prouhet-Tarry-Escott problem 

      Caley, Timothy (University of Waterloo, 2013-01-15)
      Given natural numbers n and k, with n>k, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of Z, say X={x_1,...,x_n} and Y={y_1,...,y_n}, such that x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for i=1,...,k. ...
    • Sparse Automatic Sets 

      Albayrak, Seda (University of Waterloo, 2020-11-26)
      The theory of automatic sets and sequences arises naturally in many different areas of mathematics, notably in the study of algebraic power series in positive characteristic, due to work of Christol, and in Derksen's ...
    • Variations on the Erdos Discrepancy Problem 

      Leong, Alexander (University of Waterloo, 2012-01-04)
      The Erdős discrepancy problem asks, "Does there exist a sequence t = {t_i}_{1≤i<∞} with each t_i ∈ {-1,1} and a constant c such that |∑_{1≤i≤n} t_{id}| ≤ c for all n,c ∈ ℕ = {1,2,3,...}?" The discrepancy of t equals ...

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