This book arose from a course of lectures given by the first author
during the winter term 1977/1978 at the University of Munster (West
Germany). The course was primarily addressed to future high school
teachers of mathematics; it was not meant as a systematic
introduction to number theory but rather as a historically
motivated invitation to the subject, designed to interest the
audience in number-theoretical questions and developments. This is
also the objective of this book, which is certainly not meant to
replace any of the existing excellent texts in number theory. Our
selection of topics and examples tries to show how, in the
historical development, the investigation of obvious or natural
questions has led to more and more comprehensive and profound
theories, how again and again, surprising connections between
seemingly unrelated problems were discovered, and how the
introduction of new methods and concepts led to the solution of
hitherto unassailable questions. All this means that we do not
present the student with polished proofs (which in turn are the
fruit of a long historical development); rather, we try to show how
these theorems are the necessary consequences of natural questions.
Two examples might illustrate our objectives."
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