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Fourth power diophantine equations in Gaussian integers

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Abstract

In this paper, we examine a class of fourth power diophantine equations of the form \(x^4+kx^2y^2+y^4=z^2\) and \(ax^4+by^4=cz^2\), in the Gaussian integers, where a and b are prime integers.

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Acknowledgements

The authors are indebted to the anonymous reviewer of an earlier paper for providing insightful comments and providing directions for additional work which has resulted in this paper.

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Correspondence to Farzali Izadi.

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Communicating Editor: S D Adhikari

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Izadi, F., Rasool, N.F. & Amaneh, A.V. Fourth power diophantine equations in Gaussian integers. Proc Math Sci 128, 18 (2018). https://doi.org/10.1007/s12044-018-0390-7

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  • DOI: https://doi.org/10.1007/s12044-018-0390-7

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2010 Mathematics Subject Classification

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