The Theory of Numbers

Description

Chapter I. DIVISORS AND PRIME NUMBERS 1.1 DIVISORS AND THE DIVISION ALGORITHM 1.2 DIFFERENT BASES 1.3 THE GREATEST COMMON DIVISOR OF TWO INTEGERS 1.4 THE EQUATION ax + by = n 1.5 THE G.C.D. 0F MORE THAN TWO INTEGERS 1.6 THE LEAST COMMON MULTIPLE 1.7 PRIMES 1.8 THE FUNDAMENTAL THEOREM AND SOME APPLICATIONS 1.9 THE BRACKET FUNCTION AND BINOMIAL COEFFICIENTS Chapter II. FUNDAMENTAL PROPERTIES OF CONGRUENCE 2.1 CONGRUENCE AND RESIDUES 2.2 THE ¢-FUNCTION AND REDUCED RESIDUE SYSTEMS 2.3 2.4 2.5 2.6 2.7 THE ORDER OF AN INTEGER MODULO m PERIODIC DECIMALS LINEAR CONGRUENCES WILSON’S THEOREM AND EULER’S CRITERION SIMULTANEOUS LINEAR CONGRUENCES Chapter III. POLYNOMIAL CONGRUENCES AND 3.1 3.2 3.3 3.4 3.5 PRIMITIVE ROOTS POLYNOMIAL CONGRUENCES POLYNOMIAL CONGRUENCES MODULO A PRIME POLYNOMIAL CONGRUENCES MODULO A POWER OF A PRIME PRIMITIVE ROOTS INDICES Chapter IV. QUADRATIC RESIDUES 4.1 4.2 4.3 4.4 SOME INTRODUCTORY REMARKS THE LEGENDRE SYMBOL AND A LEMMA 0F GAUSS THE LAW OF QUADRATIC RECIPROCITY SOME APPLICATIONS Chapter V. CONTINUED FRACTIONS 5.1 5.2 5.3 5.4 ' 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 FINITE CONTINUED FRACTIONS EXPANSION OF A RATIONAL NUMBER EVALUATION OF A SIMPLE CONTINUED FRACTION THE EQUATION ca: + dy = 1 INFINITE CONTINUED FRACTIONS EXPANSION OF AN IRRATIONAL NUMBER APPROXIMATION BY RATIONAL NUMBERS- QUADRATIC IRRATIONALITIES PERIODIC CONTINUED FRACTIONS PURELY PERIODIC CONTINUED FRACTIONS THE CONTINUED FRACTION EXPANSION 0F V71 THE EQUATION x2 — dy2 = 1 REFERENCES