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
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, 200