The Theory of Numbers

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