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Integers form the basis of all mathematics, and prime numbers form the basis of integers. The study of integer operations is included in the field of mathematics known as number theory. Within number theory, a special theory focused entirely on the divisibility of integers has been developed this is the theory of congruences. In this book we will review mathematical concepts pertaining to integers (and to prime numbers in particular), and we will present the theory of congruences. The material in this book is organized and presented in a manner designed to make this a comprehensive reference work on congruence theory. Most of the sources for this book are given in the references at the end of the book.
Integer Concepts.
Integer Operations.
Congruence Concepts.
Basic Congruence Operations.
Linear Congruences.
Order, Primitive Roots, and Indices of Integers.
Quadratic and Higher Order Congruences.
Appendix A The Greek Alphabet.
Appendix B Verification Procedures.
Appendix C Summary of Propositions.
Appendix D Prime Numbers &lt 10000.
Appendix E Prime Factors of Natural Numbers ≤ 1000.
Appendix F Euler’s φ(n) Function for n = 1− 250.