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Displaying similar documents to “Second order strong divisibility sequences in an algebraic number field”

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 .

Algebraic S-integers of fixed degree and bounded height

Fabrizio Barroero (2015)

Acta Arithmetica

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Let k be a number field and S a finite set of places of k containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of S-integers of k. Moreover, we give an asymptotic formula for the number of S̅-integers of bounded height and fixed degree over k, where S̅ is the set of places of k̅ lying above the ones in S.