Elementary number theory

Includes bibliographical references and index.

Preliminaries -- Primes -- Congruence's, roots and indices -- Quadratic reciprocity -- Polynomials and polynomials functions -- Combinatorics.

Number theory is a fascinating branch of mathematics that, like many other advanced desciplines od mathematics, involves a well-rounded knowledge of subjects such as algebra and arithmetic. Number Theory, the analysis of integers, is the oldest, and also the highest , branch of pure mathematics. There are many questions to be asked about the individual numbers and their property, the function of numbers, the relationship between numbers, sets of numbers, trends in sequences of numbers, and so on. Number Theory is renowned for creating easy-to-ask, hard-to-answer questions, and that's one of the reasons for its success. The main aim of number theory is to discover interesting and unexpected relationships between different types of numbers and to prove that these relationships are real. Some of the best places to start researching number theory are the key differentiators between even and odd numbers, one of which can be evenly divided and the other of which cannot be divided, and the properties of prime numbers. The objectives of this book are to expose students to this beautiful theory, to understand what inspired this quote from Gauss, and to allow students to experience mathematics as a creative, empirical science.