Browsing Mathematics (Faculty of) by Subject "number theory"
Now showing items 19 of 9

Computational Methods for Combinatorial and Number Theoretic Problems
(University of Waterloo, 20170427)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 NumberTheoretic Functions over Consecutive Integers
(University of Waterloo, 20090430)This thesis will survey a group of problems related to certain numbertheoretic 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
(University of Waterloo, 20121218)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 (3AP). Since then the bound originally given by Roth has been ... 
Multiplicities of Linear Recurrence Sequences
(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
(University of Waterloo, 20070927)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 Noneventually Periodic badic Expansions
(University of Waterloo, 20100518)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 ProuhetTarryEscott problem
(University of Waterloo, 20130115)Given natural numbers n and k, with n>k, the ProuhetTarryEscott (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
(University of Waterloo, 20201126)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
(University of Waterloo, 20120104)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 ...