## Content of Number Theory: Structures, Examples, and Problems

I STRUCTURES, EXAMPLES, AND PROBLEMS

1 Divisibility

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

12 Divisibility

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.

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