During the lecture elementaries of the modulo arithmetic, including intuitions and applications in problems, particularly in number theory, will be explained. We will also tell about the practical applications, in particular those from XX and XXI century, like the algorithms checking the correctness of control numbers (e.g. in account numbers) or ciphers. In the final part of the talk we will talk about the RSA - a cryptographical algorithm, used in bank transfers and digital document signing.