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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| Sprache: | eng |
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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}. |
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| DOI: | 10.48550/arxiv.1202.2267 |