Solving some specific tasks by Euler's and Fermat's Little theorem

Abstract

Euler's and Fermat's Little theorems have a great use in number theory. Euler's theorem is currently widely used in computer science and cryptography, as one of the current encryption methods is an exponential cipher based on the knowledge of number theory, including the use of Euler's theorem. Therefore, knowing the theorem well and using it in specific mathematical applications is important. The aim of our paper is to show the validity of Euler's theorem by means of linear congruences and to present several specific tasks which are suitable to be solved using Euler's or Fermat's Little theorems and on which the principle of these theorems can be learned. Some tasks combine various knowledge from the field of number theory, and are specific by the fact that the inclusion of Euler's or Fermat's Little theorems to solve the task is not immediately apparent from their assignment.