Elementary Number Theory

The great Carl Friedrich Gauss once wrote, "Mathematics is the queen of sciences and arithmetic the queen of mathematics." What Gauss called arithmetic, we now call number theory. This text is an extensive update of an original manuscript by Professor W. Edwin Clark (now Emeritus) of the University of South Florida, written in 2002 and made freely available on his website. It is designed for a one-semester undergraduate course and for self study.

Combinatorics and Discrete Mathematics Mathematics

Author: Mike Barrus & W. Edwin Clark
Publisher: University of Rhode Island
Source: LibreTexts
License: CC BY-NC-SA
Language: EN
Category: Basic Sciences

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Contents· 35 sections

01: Chapters
1.01: What is Number Theory
1.02: Basic Axioms for Z
1.03: Proof by Induction
1.04: Elementary Divisibility Properties
1.05: The Division Algorithm
1.06: The Floor and Ceiling of a Real Number
1.07: Greatest Common Divisor and Least Common Multiple
1.08: The Euclidean Algorithm
1.09: Bezout's Lemma
1.10: Computing Coefficients for Bezout's Lemma
1.11: Prime Numbers
1.12: Unique Factorization
1.13: The Gaussian Integers
1.14: Fermat Primes and Mersenne Primes
1.15: Number Theoretic Functions
1.16: Perfect Numbers and Mersenne Primes
1.17: Congruences
1.18: Divisibility Tests for 2 3 5 9 11
1.19: Divisibility Tests for 7 and 13
1.20: More Properties of Congruences
1.21: Residue Classes and the Integers Modelo m
1.22: The Groups Um
1.23: Chinese Remainder Theorem
1.24: Theorems of Wilson Euler and Fermat
1.25: Primality Tests
1.26: Computation of a mod m
1.27: The RSA Scheme
1.28: Sum of Squares
1.29: Epilogue
02: Appendices
2.01: Prime Numbers less than 200
2.02: Prime Numbers Up to 400
2.03: A Rings and Groups
2.4: Bibliography