This book is addressed to Students of A.E.I. who attend the course "Number Theory", either as a stand-alone course, or as a chapter of the course "Algebra I" and to those preparing for the Mathematical Olympiads.

It is a book of solved exercises which, however, are classified into six chapters with titles: Natural numbers - Integers - Divisibility - M.K.D. - E.K.P. - Arithmetic functions - Equivalencies (Equivalences) - Topics of Mathematical Olympiads.

The exercises are analytically solved and show great "self-reliance", that is, with references at the end of each exercise, all the necessary clarifications of the relevant theory are given. Among the exercises are also various suggestions that have been given from time to time as exam subjects in various Universities in our country or abroad.
It was thought appropriate to mention some of the famous unsolved problems of number theory, as well as facts about the "behavior" and multiplicity of certain forms of natural numbers (prime, perfect, friendly, etc.).