Content of Number Theory: Structures, Examples, and Problems
I STRUCTURES, EXAMPLES, AND PROBLEMS
2 Powers of Integers
3 Floor Function and Fractional Part
4 Digits of Numbers
5 Basic Principles in Number Theory
6 Arithmetic Functions
7 More on Divisibility
8 Diophantine Equations
9 Some special problems in number theory
10 Problems Involving Binomial Coefficients
11 Miscellaneous Problems
II SOLUTIONS TO PROPOSED PROBLEMS
13 Powers of Integers
14 Floor Function and Fractional Part
15 Digits of Numbers
16 Basic Principles in Number Theory
17 Arithmetic Functions
18 More on Divisibility
19 Diophantine Equations
20 Some special problems in number theory
21 Problems Involving Binomial Coefficients
22 Miscellaneous Problems
Key features of Number Theory: Structures, Examples, and Problems:
- A rigorous exposition starts with the natural numbers and the basics.
- Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties.
- Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered.
- Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems.
- Glossary, bibliography, and comprehensive index round out the text.
Download Number Theory: Structures, Examples, and Problems by Titu Andreescu, Dorin Andrica in free pdf format.