On The Solutions of The Equation (4^n)^x+p^y=z^2

On The Solutions of The Equation (4^n)^x+p^y=z^2

In this paper, we gave solutions of the Diophantine equations 16^{x}+p^{y}=z^{2}, 64^{x}+p^{y}=z^{2} where p is an odd prime, n is a positive integer and x,y,z are non-negative integers. Finally we gave a generalization of the Diophantine equation (4^{n})^{x}+p^{y}=z^{2}.

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Veröffentlicht in:arXiv.org 2012-02
Hauptverfasser: Peker, Bilge, Cenberci, Selin Inag
Format: Artikel
Sprache:eng
Schlagworte:
Diophantine equation
Integers
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Zusammenfassung:In this paper, we gave solutions of the Diophantine equations 16^{x}+p^{y}=z^{2}, 64^{x}+p^{y}=z^{2} where p is an odd prime, n is a positive integer and x,y,z are non-negative integers. Finally we gave a generalization of the Diophantine equation (4^{n})^{x}+p^{y}=z^{2}.
ISSN:2331-8422