Elementary Number Theory I

Course content

Primitive roots of an integer, Integers n for which Z_N^ * is cyclic Theory of indìces, Quadratic residues; Legendre symbol, Quadratic Reciprocity Law, Solving quadratic congruences. Perfect numbers, Mersenne primes, Fermat numbers Fibonacci numbers, Linear Diophantine equations, Pythagorean triples, Quadratic Diophantine equation. Fermat`s Infinite descent (x^4+-y^4=z^2 equations), Representing integers as sums of squares, Pell`s equation, Finite and infinite continued fractions Solving Pell`s equation using continued fractions.