Number Theory I

Course content

Primitive roots of an integer, Integers n for which Z_n^* is cyclic, Theory of indices, 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 equations, 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.