Contents

Distribution o f the Problem s accordin g t o Thei r Topic s i x

Preface x i

Part 1. Ke y Element s fro m th e Theor y 1

Notations 3

Some Classica l Form s o f Argument 3

Inequalities 3

Divisibility 4

Prime Number s 5

Congruences 6

The Functio n [x] 7

Arithmetical Function s 8

Diophantine Equation s 10

Quadratic Reciprocit y 10

Continued Fraction s 11

Classification o f Real Number s 12

Two Conjecture s 12

Part 2 . Statement s o f th e Problem s 13

Mathematical Inductio n an d Combinatoric s 15

Divisibility 19

Prime Number s 2 5

Representation o f Numbers 3 4

Congruences 3 8

Primality Test s an d Factorizatio n Algorithm s 4 4

Integer Part s 4 9