On the Diophantine equation $x^{2}-kxy+y^{2}-2^{n}=0$

Title:

On the Diophantine equation $x^{2}-kxy+y^{2}-2^{n}=0$

Creator:

Keskin, Refik, Şiar, Zafer, and Karaatlı, Olcay

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:051cb44c-9048-4e81-9af8-844c60dbd853
uuid:051cb44c-9048-4e81-9af8-844c60dbd853

Subject:

Diophantine equation, Pell equation, generalized Fibonacci number, and generalized Lucas number

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

783-797

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:3

Harvested from:

CDK

Metadata only:

false