# Introduction to Number Theory

## Objectives

The student is supposed to learn the basic concepts of elementary number theory.

## General characterization

##### Code

10838

##### Credits

6.0

##### Responsible teacher

Joaquim Eurico Anes Duarte Nogueira

##### Hours

Weekly - 5

Total - 70

##### Teaching language

Português

### Prerequisites

None.

### Bibliography

Burton, David, Elementary Number Theory, 2nd ed., Wm. C. Brown, Dubuque, IA, 1989.

Tattersall, James - Elementary Number Theory in Nine Chapters, 2th edition, Cambridge University Press, 2005.

Ore, Oysten., An Invitation to Number Theory, Mathematical Association of America, Washington, DC, 1967.

Sierpinski, W., Elementary Theory of Numbers, North-Holland, Amsterdam, 1988.

G.H.Hardy, E.M.Wright, Theory of numbers.

### Teaching method

There are classes in which theory is lectured and illustrated by examples. There are also problem-solving sessions. Some exercises are left to the students to be solved on their own as part of their learning process.

### Evaluation method

Available soon

## Subject matter

- Divisibility
- Prime numbers
- Euclidean algorithm
- Fundamental thorem of arithmetic
- Factorization methods
- Diophantine equations. Pythagorean triples
- Congruences and modular arithmetic
- Linear modular equations. Polynomial equations.
- Chinese remainder theorem
- Wilson´s theorem and Fermat´s theorem
- Euler´s theorem and function
- Perfect numbers
- Quadratic reciprocity
- Continued fractions
- Arithmetic functions
- Open problems