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Pell-Gleichung. Geschichtliche Entwicklung und Kettenbruchzerlegung

Pell-Gleichung. Geschichtliche Entwicklung und Kettenbruchzerlegung

          
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About the Book

Examensarbeit aus dem Jahr 2010 im Fachbereich Mathematik - Zahlentheorie, Note: 1,0, Eberhard-Karls-Universität Tübingen (Mathematisches Institut), Sprache: Deutsch, Abstract: Die Zahlentheorie ist ein Teilgebiet der Mathematik, welche sich im weitesten Sinne mit den Eigenschaften der Zahlen beschäftigt. Zu diesem Teilgebiet gehört unter anderem auch die Lehre von den diophantischen Gleichungen. Eine diophantische Gleichung ist eine Polynomfunktion in x, y, z, ..., bei der als Lösungen nur ganze Zahlen erlaubt sind. Die spezielle diophantische Gleichung der Form x2 - dy2 = 1 mit x, y ∈ Z und d eine nicht-quadratische Zahl, heißt Pell-Gleichung. Anzumerken ist, dass (±1, 0) immer eine triviale Lösung ist und außerdem darf d nicht quadratisch sein, andernfalls würde man wieder (±1, 0) als triviale Lösung erhalten. Die Bezeichnung der Pell-Gleichung geht auf den englischen Mathematiker John Pell zurück, der 1611 in Sussex geboren wurde und 1685 in London verstorben ist. Das Auffinden von ganzzahligen Lösungen der Pell-Gleichung hat viele Mathematiker Jahrhundertelang beschäftigt. Schon Archimedes (ca. 287 v. Chr - 212 v. Chr) und Diophantus untersuchten ähnliche Fragestellungen. Aber erst mit Langrange waren alle Fragen, die man sich für das Lösen der Pell-Gleichung gestellt hatte, geklärt. Zunächst verschaffen wir uns einen kurzen Überblick über die geschichtliche Entwicklung der Pell-Gleichung. Im zweiten Kapitel werden wir die Kettenbruchtheorie kennenlernen, sodass wir im dritten Kapitel diese Theorie auf die Pell-Gleichung anwenden können, was uns dann eine Lösung der Pell-Gleichung liefert. Zum Schluss wenden wir uns zur Veranschaulichung noch einigen Beispielen zu.


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Product Details
  • ISBN-13: 9783668352292
  • Publisher: Grin Publishing
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 4 mm
  • Width: 148 mm
  • ISBN-10: 3668352291
  • Publisher Date: 30 Nov 2016
  • Height: 210 mm
  • No of Pages: 72
  • Series Title: German
  • Weight: 104 gr


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