1. komponenta

Lecture type	Total
Lectures	30
Exercises	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: The course will cover the basic notions from elementary number theory. Special attention will be given to topics relevant for mathematical competitions.

COURSE DESCRIPTION AND SYLLABUS:
1. Divisibility. Greatest common divisor. Euclidean algorithm. Primes. Unique factorization.
2. Congruences. Linear congruences. Linear diophantine equations. Chinese remainder theorem. Euler's theorem. Wilson's theorem. Primitive roots.
3. Problems from mathematical competitions I.
4. Arithmetic functions. Floor function. Number and sum of divisors. Euler's function. Mobius function. Distribution of primes.
5. Quadratic residues and quadratic forms. Legendre symbol. Quadratic reciprocity law. Sums of two and four squares.
6. Diophantine equations. Pythagorean triples. Pell equation. Continued fractions. Diophantine approximations.
7. Problems from mathematical competitions II.
8. Applications of number theory. Introduction to cryptography. Primality tests. Factoring methods.

Enrollment :
Passed : Introduction to mathematics

Mandatory course - Regular study - Mathematics Education