Equations and Inequations

Equations and Inequalities

Elementary Problems and Theorems in Algebra and Number Theory
Translated by Karl Dilcher

CONTENTS

I. Algebraic Identities and Equations
1- Formulas for Powers
2- Finite Sums
3- Polynomials
4- Symmetric Polynomials
5- Systems of Equations
6- Irrational Equations
7- Some Applications of Complex Numbers

II. Algebraic Inequalities
1- Definitions and Properties
2- Basic Methods
3- The Use of Algebraic Formulas
4- The Method of Squares
5- The Discriminant and Cauchy's Inequality
6- The Induction Principle
7- Chebyshev's Inequality
8- Inequalities Between Means
9- Appendix on Irrational Numbers

III. Number Theory
1- Basic Concepts
2- Prime Numbers
3- Congruences
4- Congruences in One Variable
5- Diophantine Equations
6- Solvability of Diophantine Equations
7- Integer Part and Fractional Part
8- Base Representations
9- Dirichlet's Principle
10- Polynomials

IV. Hints and Answers
1- Hints and Answers to Chapter 1
2- Hints and Answers to Chapter 2
3- Hints and Answers to Chapter 3 .