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Czechoslovak Mathematical Journal

, Volume 63, Issue 3, pp 783–797 | Cite as

On the Diophantine equation x 2kxy + y 2 − 2 n = 0

  • Refik Keskin
  • Zafer Şiar
  • Olcay Karaatli
Article
  • 208 Downloads

Abstract

In this study, we determine when the Diophantine equation x 2kxy+y 2−2 n = 0 has an infinite number of positive integer solutions x and y for 0 ⩽ n ⩽ 10. Moreover, we give all positive integer solutions of the same equation for 0 ⩽ n ⩽ 10 in terms of generalized Fibonacci sequence. Lastly, we formulate a conjecture related to the Diophantine equation x 2kxy + y 2 − 2 n = 0.

Keywords

Diophantine equation Pell equation generalized Fibonacci number generalized Lucas number 

MSC 2010

11B37 11B39 11B50 11B99 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013

Authors and Affiliations

  1. 1.Sakarya UniversitySakaryaTurkey
  2. 2.Bilecik Şeyh Edebali UniversityBilecikTurkey
  3. 3.Sakarya UniversitySakaryaTurkey

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