The book on elementary number theory consists of articles, many of which were published in the Kvant journal. Euclid's algorithm, the main theorem of arithmetic, Farey series, periodic fractions, Fibonacci numbers, Fermat's small theorem, chain fractions, the quadratic reciprocity law have been studied in great detail, with a large number of examples and exercises. It can serve as a tutorial for math classes and circles. Addressed to schoolchildren in grades 7-11, teachers, as well as all lovers of mathematics.