Book description
A highly successful presentation of the fundamental concepts of number theory and computer programming
Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highlyqualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area.
Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most wellknown theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the publicprivate key system of cryptography. In addition, the book includes:
Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas
Select solutions to the chapter exercises in an appendix
Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set
A related website with links to select exercises
An Instructor's Solutions Manual available on a companion website
Elementary Number Theory with Programming is a useful textbook for undergraduate and graduatelevel students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.
Table of contents
 COVER
 TITLE PAGE
 PREFACE
 WORDS
 NOTATION IN MATHEMATICAL WRITING AND IN PROGRAMMING
 1 SPECIAL NUMBERS: TRIANGULAR, OBLONG, PERFECT, DEFICIENT, AND ABUNDANT
 2 FIBONACCI SEQUENCE, PRIMES, AND THE PELL EQUATION
 3 PASCAL’S TRIANGLE

4 DIVISORS AND PRIME DECOMPOSITION
 DIVISORS
 GREATEST COMMON DIVISOR
 DIOPHANTINE EQUATIONS
 LEAST COMMON MULTIPLE
 PRIME DECOMPOSITION
 SEMIPRIME NUMBERS
 WHEN IS A NUMBER AN mTH POWER?
 TWIN PRIMES
 FERMAT PRIMES
 ODD PRIMES ARE DIFFERENCES OF SQUARES
 WHEN IS n A LINEAR COMBINATION OF a AND b?
 PRIME DECOMPOSITION OF n!
 NO NONCONSTANT POLYNOMIAL WITH INTEGER COEFFICIENTS ASSUMES ONLY PRIME VALUES
 EXERCISES

5 MODULAR ARITHMETIC
 CONGRUENCE CLASSES MOD k
 LAWS OF MODULAR ARITHMETIC
 MODULAR EQUATIONS
 FERMAT’S LITTLE THEOREM
 FERMAT’S LITTLE THEOREM
 MULTIPLICATIVE INVERSES
 WILSON’S THEOREM
 WILSON’S THEOREM
 WILSON’S THEOREM (2ND VERSION)
 SQUARES AND QUADRATIC RESIDUES
 LAGRANGE’S THEOREM
 LAGRANGE’S THEOREM
 REDUCED PYTHAGOREAN TRIPLES
 CHINESE REMAINDER THEOREM
 CHINESE REMAINDER THEOREM
 EXERCISES
 6 NUMBER THEORETIC FUNCTIONS

7 THE EULER PHI FUNCTION
 THE PHI FUNCTION
 EULER’S GENERALIZATION OF FERMAT’S LITTLE THEOREM
 PHI OF A PRODUCT OF m AND n WHEN gcd(m,n) > 1) > 1
 THE ORDER OF a (mod n)
 PRIMITIVE ROOTS
 THE INDEX OF m (mod p) RELATIVE TO a
 TO BE OR NOT TO BE A QUADRATIC RESIDUE
 THE LEGENDRE SYMBOL
 QUADRATIC RECIPROCITY
 LAW OF QUADRATIC RECIPROCITY
 WHEN DOES x2 = a (mod n) HAVE A SOLUTION?
 EXERCISES
 8 SUMS AND PARTITIONS
 9 CRYPTOGRAPHY
 ANSWERS OR HINTS TO SELECTED EXERCISES
 INDEX
 END USER LICENSE AGREEMENT
Product information
 Title: Elementary Number Theory with Programming
 Author(s):
 Release date: June 2015
 Publisher(s): Wiley
 ISBN: 9781119062769
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