Introduction to Number Theory
Code
10838
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Manuel Almeida Silva
Weekly hours
5
Total hours
70
Teaching language
Português
Objectives
The student is supposed to learn the basic concepts of elementary number theory.
Prerequisites
None.
Subject matter
- Divisbility
- Prime numbers
- Euclidean algorithm
- Fundamental thorem of arithmetic
- Factorization methods
- Diophantine equations. Pythagorean triples
- Congrueneces 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
Bibliography
A. Gareth Jones, J. Jones, Elementary Number Theory
William Stein, Elementary Number Theory: Primes, Congruences, and Secrets (2011)
José Plínio de Oliveira Santos, Introdução à Teoria dos Números, IMPA 2009
H. Davenport, The Higher arithmetic, Cambridge, 2008
G.H.Hardy, E.M.Wright, Theory of numbers
Vinogradov, I. M., Elements of Number Theory, NY Dover, 2003
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.