Filip Najman
Published 2010-05-10Version 1
In this note we find all the solutions of the Diophantine equation $x^4\pm y^4=iz^2$ using elliptic curves over $\mathbb Q(i)$. Also, using the same method we give a new proof of Hilbert's result that the equation $x^4\pm y^4=z^2$ has only trivial solutions in Gaussian integers.
Comments: 5 pages, to appear in Amer. Math. Monthly
Journal: Amer. Math. Monthly 117 (2010), 637-641
On the Diophantine equation $(x+1)^{k}+(x+2)^{k}+...+(2x)^{k}=y^n$
The Diophantine Equation $x^4 + 2 y^4 = z^4 + 4 w^4$---a number of improvements
Polynomial parametrization of the solutions of Diophantine equations of genus 0
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