The Diophantine equation $x^4\pm y^4=iz^2$ in Gaussian integers (1005.1528v1)

Published 10 May 2010 in math.NT

Abstract: 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.

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Generate a whiteboard explanation of this paper.

Sign Up to Generate

Video Overview

Generate a video overview of this paper.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (1)

Filip Najman

Collections

Sign up for free to add this paper to one or more collections.