A Friendly Introduction to Number Theory | Fourth Edition | By Pearson (Paperback)  | Released: 03-Jun-19

A friendly introduction to number theory, 4th edition is designed to introduce students to the overall themes and methodology of Mathematics through the detailed study of one particular facet-number theory. Starting with nothing more than basic high school Algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analysed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results. Table of Contents: br>Chapter 1: What is number theory? Br>chapter 2: Pythagorean triples br>Chapter 3: Pythagorean triples and the br>Unit circle br>Chapter 4: sums of higher powers and fermat?s last theorem br>Chapter 5: Divisibility and the greatest common divisor br>Chapter 6: Linear Equations and the greatest common divisor br>Chapter 7: factorization and the fundamental theorem of Arithmetic br>Chapter 8: congruences br>Chapter 9: congruences, powers, and fermat?s little theorem br>Chapter 10: congruences, powers, and euler?s formula br>Chapter 11: euler?s Phi function and the Chinese Remainder theorem br>Chapter 12: prime numbers br>Chapter 13: counting primes br>Chapter 14: Mersenne primes br>Chapter 15: Mersenne primes and perfect numbers br>Chapter 16: powers modulo M and successive Squaring br>Chapter 17: computing kth roots modulo M br>Chapter 18: powers, roots, and ?unbreakable? codes br>Chapter 19: primality testing and Carmichael numbers br>Chapter 20: squares modulo br br>Chapter 21: is -1 a Square modulo br? Is 2? Br>chapter 22: Quadratic Reciprocity br>Chapter 23: proof of Quadratic Reciprocity br>Chapter 24: which primes are sums of two squares? Br>chapter 25: which numbers are sums of two squares? Br>chapter 26: as easy as one, two, three br>Chapter 27: euler?s Phi function and sums of divisors br>Chapter