On the algebraic difference equations  in , related to a family of elliptic quartics in the plane.

Bastien, G.; Rogalski, M.

Displaying similar documents to “On the algebraic difference equations $u_{n + 2} u_{n} = ψ (u_{n + 1})$ in $ℝ_{*}^{+}$ , related to a family of elliptic quartics in the plane.”

Large time-stepping spectral methods for the semiclassical limit of the defocusing nonlinear Schrödinger equation.

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Two conservative difference schemes for the generalized Rosenau equation.

Hu, Jinsong, Zheng, Kelong (2010)

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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 $0 \leq n \leq 10 .$ 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 $x^{2} - k x y + y^{2} - 2^{n} = 0$ .