Elementary Number Theory in Nine Chapters

  title={Elementary Number Theory in Nine Chapters},
  author={James J. Tattersall},
1. The intriguing natural numbers 2. Divisibility 3. Prime numbers 4. Perfect and amicable numbers 5. Modular arithmetic 6. Congruences of higher degree 7. Cryptography 8. Representations 9. Partitions Tables Answers to selected exercises Bibliography. 
Problems in Elementary Number Theory
1. Preface 2 2. Notations and Abbreviations 3 3. Divisibility Theory I 4 4. Divisibility Theory II 8 5. Arithmetic in Zn 11 6. Primes and Composite Numbers 13 7. Rational and Irrational Numbers 15 8.
A basic characteristic of twin primes and its generalization
The sum of powers of positive divisors of an integer, expressed in terms of the floor function, provides the basis for another characterization of twin primes in particular, and of prime k-tuples
Note on Perfect Numbers and their Existence
This paper will address the interesting results on perfect numbers. As we know that, perfect number ends with 6 or 8 and perfect numbers had some special relation with primes. Here one can understand
Generating Tuples of Integers Modulo n
In this paper, p 2 Z Z p p + - @ for n ≥ 3, where p=2n-1 and Zp-1 p =e (e is the multiplicative identity). The diagonal elements of Z+ 2n+1 can generate Z2k-2 2n-1; k=2, 3,… n-1 by simple algorithm.
Balancing Numbers and Application
  • Ramesh Gautam
  • Mathematics
    Journal of Advanced College of Engineering and Management
  • 2018
 In this paper, we present about origin of Balancing numbers; It!s connection with Triangular, Pells numbers, and Fibonacci numbers; beginning with connections of balancing numbers with other numbers
The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4
Let D ≠ 1 be a positive non-square integer. In this paper are given the proofs for two conjectures related to Pell’s equation x −Dy = ± 4, proposed by A. Tekcan. Keywords— Pell’s equation, solutions
Number Theory: Structures, Examples, and Problems
Fundamentals.- Divisibility.- Powers of Integers.- Floor Function and Fractional Part.- Digits of Numbers.- Basic Principles in Number Theory.- Arithmetic Functions.- More on Divisibility.-
[DOC] Elementary Theory Of Numbers
Elementary Number Theory: Primes, Congruences, and Secrets-William Stein 2008-10-28 This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to
For k2 N we deflne a new divisor function sk called the k th prime symmetric function. By analogy with the sum of divisors function ae, we use the functions sk to consider variations on perfect
A Note on Boolean Lattices and Farey Sequences III
We establish monotone bijections between subsequences of the Farey sequences and the halfsequences of Farey subsequences associated with elements of the Boolean lattices.