Congruences Module m and its Applications and Diophantine Equations

Abstract

A method of analysis of two topics of the theory of numbers, the congruences modulo m and the Diophantine equations, is developed; the first referred to the divisibility between numbers, and the second to the solution of equations with integer coefficients with solutions in (integer) numbers. Prime numbers and the decomposition of an integer into prime factors are studied, as well as the knowledge of divisibility and its properties. Likewise, the application of both topics for the encryption of information in an example of a word with 10 (ten) non-repeated letters, which gives rise to an unintelligible phrase, which can be used as a security code.