O pequeno teorema de Fermat e de Euler para inteiros gaussianos

Abstract

In this paper we will study the set of gaussian integer, which is formed by the numbers of the form a + bi , where a and b are integers. We will recall some important properties of integers and extend them to set of gaussian integers, such as divisibility, euclidean division, factorization and modular arithmetic. Next, we present a classification for Gaussian prime, that is, which Gaussian integers are prime. And finally, we will give a version of Fermat’s Little Theorem and Euler’s Theorem and a closed formula for calculating Euler’s phi function for every Gaussian integer.