Moody, D.
and Zargar, A.
(2013),
On integer solutions of x^4+y^4-2z^4-2w^4=0, Notes on Number Theory and Discrete Mathematics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=913962
(Accessed April 19, 2024)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
On integer solutions of x^4+y^4-2z^4-2w^4=0
Published
Author(s)
, Arman S. Zargar
Abstract
In this article, we study the quartic Diophantine equation x^4+y^4-2z^4-2w^4=0. We find non-trivial integer solutions. Furthermore, we show that when a solution has been found, a series of other solutions can be derived. We do so using two different techniques. The first is a geometric method due to Richmond, while the second involves elliptic curves.Citation
Notes on Number Theory and Discrete Mathematics
Volume
19
Issue
1
Pub Type
Journals
Download Paper
Keywords
Diophantine equation, congruent elliptic curve
Citation
Created September 18, 2013, Updated June 2, 2021