Corpus ID: 201234323

# Elementary Number Theory

```@inproceedings{Jones1976ElementaryNT,
title={Elementary Number Theory},
author={Gareth A. Jones},
year={1976}
}```
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.
443 Citations
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
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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
• Mathematics
• 2008
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
• Mathematics
• 2016
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
• Mathematics
• 2017
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
SOLUTIONS OF THE CUBIC FERMAT EQUATION IN QUADRATIC FIELDS
• Mathematics
• 2013
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