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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."
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."
Dieses Buch ist aus einer Vorlesung entstanden, die vom ersten der
bei- den Verfasser im Wintersemester 1977/78 an der Universitat
Munster ge- halten wurde. In dieser Vorlesung, die sich vor allem
an Lehrerstuden- ten wandte, ging es nicht so sehr urn
systematische Wissensvermittlung, sondern darum, Interesse an
zahlentheoretischen Fragestellungen und Entwicklungen zu wecken,
wobei vor allem historische Zusarnrnenhange in den Vordergrund
gestellt wurden. Bei dieser Zielsetzung ist auch das Buch
geblieben, das keines der vie len vorhandenen ausgezeichneten Bu-
cher uber Zahlentheorie ersetzen kann oder will. Wir versuchen, an
aus- gewahlten Beispielen zu zeigen, wie aus der Untersuchung
naheliegender zahlentheoretischer Probleme im Laufe der
geschichtlichen Entwicklung irnrner umfangreichere und tiefere
Theorien entstanden sind, wie irnrner wieder neue unerwartete
Zusarnrnenhange zwischen scheinbar ganz verschie- denen
Problemkreisen entdeckt wurden und wie die Einfuhrung neuer Metho-
den und Begriffe oft die Losung lange Zeit unangreifbar
erscheinender Probleme ermoglichte. Wir wollen also einige wichtige
Satze der Zahlen- theorie den Studierenden nicht als fertiges
Ergebnis in einer Formulie- rung und mit Beweisen, die Endprodukte
einer langen Entwicklung sind, vorsetzen, sondern wir versuchen
darzustellen, wie sich diese Satze notwendig aus naheliegenden
Fragestellungen ergeben haben.
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