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
73
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
- Linear recurrences
- Open problems
Bibliography
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
Classes consist on two different aspects: an oral explanation which is illustrated by examples and the resolution, by the students, of proposed exercises.
Students can ask for any questions either in class or during office ours.
Evaluation method
3 Tests during the semester
or
Final Exame