At the end of the course students are expected to:
Know the basic properties of greatest common divisors, apply the Euclidean algorithm to compute it and solve linear Diophantine equations,
Learn the Fundamental Theorem of Arithmetic and use prime factorization to compute greatest common divisor, least common multiple etc. Of several integers,
Find all solutions of linear congruences and systems of linear congruences (by means of Chinese remainder theorem),
Know Fermat’s little theorem and its generalization Euler’s theorem and their consequences,
Be able to derive formulas of and identities involving number theoretic functions in terms of the prime factorization of the integer,
Learn important properties of Euler’s Phi function and be aware of its application to public key cryptography.