The Diophantine equation $x^4\pm y^4=iz^2$ in Gaussian integers

In this note we find all the solutions of the Diophantine equation $x^4\pm y^4=iz^2 $u s i n g e l l i p t i c c u r v e s o v e r$ \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.

The Diophantine equation $x^{4} \pm y^{4} = i z^{2}$ in Gaussian integers

文献摘要

讨论

讲解博客

AI智能校验

The Diophantine equation $x^{4} \pm y^{4} = i z^{2}$ in Gaussian integers

文献摘要

讨论

讲解博客

AI智能校验

The Diophantine equation x4±y4=iz2x4±y4=iz2 in Gaussian integers

文献摘要

讨论

|讲解博客

|AI智能校验

The Diophantine equation x4±y4=iz2x4±y4=iz2 in Gaussian integers

文献摘要

讨论

|讲解博客

|AI智能校验

The Diophantine equation $x^{4} \pm y^{4} = i z^{2}$ in Gaussian integers

讲解博客

AI智能校验

The Diophantine equation $x^{4} \pm y^{4} = i z^{2}$ in Gaussian integers

讲解博客

AI智能校验