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SOME QUARTIC DIOPHANTINE EQUATIONS IN THE GAUSSIAN INTEGERS
Published online by Cambridge University Press: 16 June 2015
Abstract
In this paper we examine solutions in the Gaussian integers to the Diophantine equation $ax^{4}+by^{4}=cz^{2}$ for different choices of $a,b$ and $c$. Elliptic curve methods are used to show that these equations have a finite number of solutions or have no solution.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 187 - 194
- Copyright
- © 2015 Australian Mathematical Publishing Association Inc.
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