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Displaying similar documents to “A remark on the paper of I. Raitchinov 'Sur un théorème de Pólya'.”

On the Diophantine equation x 2 - k x y + y 2 - 2 n = 0

Refik Keskin, Zafer Şiar, Olcay Karaatlı (2013)

Czechoslovak Mathematical Journal

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In this study, we determine when the Diophantine equation x 2 - k x y + 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 2 - k x y + y 2 - 2 n = 0 .