In this work, several independent topics related on number theory are discussed. They are distributed into four chapters, each of . ideas and relations with the rest of the theory in order to do the topics understandble for persons who are not very. and, in general, by the wideness of number theory. The very extended idea considering number theory as a dicult branch of Mathematics is. beauty, it is the diversity of its methods, sometimes algebraic, analytic and geometric ideas converge in the same problem.