Adademisk afhandling--Lund.

"Of considerable interest among mathematicians is the problem of the determination of primality of positive integers. For a small integer, N, we may say that N is prime or composite merely by trying to divide N by all primes less than or equal to the square root of N since if N is composite, one of its factors must be [less than or equal to] the square root of N. However, if N is large this test loses its practicality and we must resort to a more feasible method. It is the purpose of this paper to trace and show the development of such methods"--Introduction. / "June, 1959." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Paul J. McCarthy, Professor Directing Paper. / Includes bibliographical references (leaf 28).

A dissertation submitted in fulfillment of the requirements for the degree of Master of Science in the school of Mathematics , University of the Witwatersrand, Johannesburg, 2018 / MT 2018

In this thesis we attempt to generalize some of Kummer's work on Fermat's Last Theorem over the rational numbers to quadratic fields. In particular, under certain congruence conditions it is shown that the Fermat equation of exponent p has no solution over Q(√m) when p is a m-regular prime. Completely analogous to the work of Kummer, it is shown that m-regular primes can be described in terms of the generalized Bernoulli numbers. When p = 3,5 and 7, an explicit, easily computable criterion is given for m-regularity. / Ph. D.

No description available.

Orientador: Emerson Alexandre de Oliveira Lima / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T21:19:45Z (GMT). No. of bitstreams: 1 Silva_FilardesdeJesusFreitasda_M.pdf: 678989 bytes, checksum: 49b0b13ce88d8aa64141c17e237d85fe (MD5) Previous issue date: 2009 / Resumo: Neste trabalho focalizamos os principais conceitos da teoria elementar dos números objetivando uma melhor compreensão das Equações Diofantinas Clássicas e suas aplicações e para isto explicitamos os conceitos de Números primos, Algoritmo de Euclides, Máximo divisor comum e Mínimo múltiplo comum, assim como a teoria das Congruências, uma abordagem sobre a Criptografica RSA e Soma de Inteiros. Palavras-Chave: Congruências Lineares, Soma de Inteiros, Equação de Fermat, Soma de Quadrados / Abstract: In this work we focus the main concepts of the elementary theory of numbers seeking a better understanding of Classical diophantine equations and their applications for this and explained the concepts of prime numbers, algorithms of Euclid, maximum common divisor and least common multiple and the theory of congruence , an approach on the RSA encryption and Sum of Integers. Keywords: Linear congruence, Sum of Integers, equation of Fermat, Sum of Squares / Mestrado / Teoria dos Numeros / Mestre em Matemática