Elementary Number Theory

Gove Effinger received his Ph.D. in Mathematics from the University of Massachusetts (Amherst) in 1981 and subsequently taught at Bates College for 5 years and then Skidmore College for 29 years. He is the author of three books: An Elementary Transition to Abstract Mathematics (with Gary L. Mullen, CRC Press), Additive Number Theory of Polynomials over a Finite Field (with David R. Hayes), and Common-Sense BASIC: Structured Programming with Microsoft Quick BASIC (with Alice M. Dean), as well as numerous research papers. His research focus has primarily been concerned with the similarities of polynomials over a finite fields and ordinary integers. Gary L. Mullen is Professor of Mathematics at the Pennsylvania State University, University Park, PA. He has taught both undergraduate and graduate courses there for over 40 years. In addition, he has written more than 150 research papers and co-authored seven books, including both graduate as well as undergraduate textbooks. He also served as department head for seven years and has served as an editor on numerous editorial boards, including having served as Editor-in-Chief of the journal Finite Fields and Their Applications since its founding in 1995.

1. Divisibility in the Integers Z 2. Prime Numbers and Factorization 3. Congruences and the Sets Zn 4. Solving Congruences 5. The Theorems of Fermat and Euler 6. Applications in Modern Cryptography 7. Quadratic Residues and Quadratic Reciprocity 8. Some Fundamental Number Theory Functions 9. Diophantine Equations 10. Finite Fields 11. Some Open Problems in Number Theory A. Mathematical Induction B. Sets of Numbers Beyond the Integers