Introduction to Number Theory
The student is supposed to learn the basic concepts of elementary number theory.
Weekly - 5
Total - 70
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.
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.
- 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
Programs where the course is taught: