Number theory 1000-135TL

1) student knows basic notions conserning the fundamental theorem of arithmetic, knows how to compute GCD of two or more numbers;
2) she/he recognizes the fundamental importance of prime nimbers in mathematics; knows the history of their investigations; is capable of proving Chebyshev's theorem and can formulate the Prime Number Theorem,
3) knows the notion of congruence in integers and can see it in the context of abstract algebra; can apply the basic theorems (little Fermats theorem, Eulers theorem, Wilsons theorem); understands the importance of congruences in contemporary cryptography.
4) can solve the simplest diophantine equations,
5) knows the quadratic reciprocity law (with elements of its history) and can apply it.
6) knows the most famous open problems in number theory; recognizes their importance in mathematics and culture.