Elementary Number Theory Burton

Elementary Number Theory is designed for the one-semester junior- or senior-level number theory course usually taken by mathematics majors who plan to teach mathematics in high school or college. In this new edition all numerical information has been updated and recent developments in number theory are indicated where appropriate. Cover 1 Contents 3 Preface 5 Timeline 8 1: Preliminaries 10 2: Divisibility 27 3: Primes 53 4: Congruences 75 5: Fermat's theorem 99 6: Functions 116 7: Euler's generalisation of F's theorem 140 8: Primitive roots & indices 161 9: Quadratic reciprocity 188 10: Perfect numbers 221 11: Fermat conjecture 244 12: Integers as sums of squares 262 13: Fibonacci nos & continued fractions 287 Prime number theorem 346 Refs 353 T1: primes 357 T2: smallest prime factors 358 T3: primes 5k-10k 368 T4: primes in intervals 370 T5: n^2,n^2 n