These lectures are intended as an introduction to the elementary theory of numbers. The word "elementary" means both in the technical sense (complex variable theory is to be avoided) and in the usual sense (that of being easy to understand).
Readers are presupposed to be familiar with the most elementary concepts of arithmetic, i.e., elementary divisibility properties, g.c.d. (greatest common divisor), l.c.m. (least common multiple), essentially unique factorizaton into primes and the fundamental theorem of arithmetic: if p | ab then p | a or p | b.
This book consists of a number of rather distinct topics, each of which could easily be the subject of 15 lectures. Hence, there shall not be any deep penetration in any direction. On the other hand, it is well known that in number theory, more than in any other branch of mathematics, it is easy to reach the frontiers of knowledge. It is easy to propound problems in number theory that are unsolved. Many of these problems shall be mentioned; but the trouble with the natural problems of number theory is that they are either too easy or much too difficult. Therefore this book shall try to expose some problems that are of interest area and unsolved but for which there is at least a reasonable hope for a solution.
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