O pequeno teorema de Fermat e de Euler para inteiros gaussianos

• Autor(a) principal: Brandão Junior, Cláudio de Oliveira
• Data de Publicação: 2019
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFMT
• Texto Completo: http://ri.ufmt.br/handle/1/4264
• topic: Inteiro Gaussiano; Norma; Pequeno teorema de Fermat; Função de Euler; Teorema de Euler; Primos Gaussianos; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA; Gaussian Integer; Norm; Fermat’s Little Theorem; Euler’s Function; Euler’s Theorem; Gaussian Prime

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.