Introduction to Number Theory

Course content

Well ordering of integers, mathematical and strong induction, Divisibility, Division algorithm, Greatest common divisor, Euclidean algorithm, Linear Diophantine equations, Prime numbers, Fundamental theorem of arithmetic, General information about Goldbach conjecture and gaps between primes and Drichlet`s theorem, Congruence modulo n, Modular arithmetic, Linear congruences, Chinese remainder theorem, Fermat`s little theorem, Wilson`s theorem, Number theoretic functions, Tau and sigma functions, Greatest integer function, Moebius inversion, Euler`s phi function, Euler`s theorem and its applications to cryptography.