Corpus ID: 201234323

Elementary Number Theory

  title={Elementary Number Theory},
  author={Gareth A. Jones},
Some preliminary considerations divisibility theory in the integers primes and their distribution the theory of congruences Fermat's theorem number-theoretic functions Euler's generalization of Fermat's theorem primitive roots and indices the quadratic reciprocity law perfect numbers the Fermat conjecture representation of integers as sums of squares Fibonacci numbers continued fractions some 20th-century developments appendices. 
A Comprehensive Course in Number Theory
Preface Introduction 1. Divisibility 2. Arithmetical functions 3. Congruences 4. Quadratic residues 5. Quadratic forms 6. Diophantine approximation 7. Quadratic fields 8. Diophantine equations 9.Expand
Quadratic Reciprocity: Proofs and Applications
The law of quadratic reciprocity is an important result in number theory. The purpose of this thesis is to present several proofs as well as applications of the law of quadratic reciprocity. I willExpand
On Giuga’s conjecture
In this paper we shall investigate Giuga’s conjecture which asserts an interesting characterization of prime numbers, just as Wilson’s Theorem. Some variations and consequences of the GiugaExpand
Quadratic reciprocity for the rational integers and the Gaussian integers
This thesis begins by giving a brief time line of the origins of Number Theory. It highlights the big theorems that have been constructed in this subject, along with the mathematicians whoExpand
Some Divisibility Properties in Ring of Polynomials over a Unique Factorization Domain
Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in theExpand
An equivalence of Ward’s bound and its application
  • Xiaoyu Liu
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 2011
This paper proves an equivalent condition of Ward's bound on dimension of divisible codes, which is part of a set of congruences having integer solutions, which makes the generalization of Ward’s bound an explicit one. Expand
On the Computation of Representations of Primes as Sums of Four Squares
Lagrange proved that every positive integer is the sum of four squares of natural numbers. Although Lagrange’s proof is constructive, it is not known whether the relative algorithm produces aExpand
Fields with indecomposable multiplicative groups
Abstract We classify all finite fields and all infinite fields of characteristic not equal to 2 whose multiplicative groups are direct-sum indecomposable. For finite fields, we obtain ourExpand
On the quartic Gauss sums and their recurrence property
The main purpose of this paper is, using the method of trigonometric sums and the properties of Gauss sums, to study the computational problem of one kind of congruence equation modulo an odd primeExpand
We give necessary and sufficient conditions on a squarefree integer d for there to be non-trivial solutions to x3 + y3 = z3 in , conditional on the Birch and Swinnerton-Dyer conjecture. TheseExpand


Elementary Number Theory
Designed for a first course in number theory with minimal prerequisites, the book is designed to stimulates curiosity about numbers and their properties. Includes almost a thousand imaginativeExpand
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THE arithmetical questions treated by Diophantus of Alexandria, who flourished about the year 250 A.D., included such problems as the solution of the equationsHistory of the Theory of Numbers.ByExpand
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THE quaint words addressed “to the great variety of readers” by the editors of the folio Shakespeare of 1623 are equally applicable to the useful compendium of mathematical history which is theExpand
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A History of Greek Mathematics
WERE this book only for the mathematician it would be no book for me; but it is a great deal more. It is for all who care for the historical aspect of science; it is for all lovers of Greek, forExpand
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