# On integer solutions of x4 + y4 – 2z4 – 2w4 = 0

Dustin Moody and Arman Shamsi Zargar
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 19, 2013, Number 1, Pages 37–43
Full paper (PDF, 164 Kb)

## Details

### Authors and affiliations

Dustin Moody
Computer Security Division, NIST
100 Bureau Drive, Gaitherburg, MD, 20899-8930

Arman Shamsi Zargar
Department of Mathematics, Azarbaijan Shahid Madani University
Tabriz, Iran

### Abstract

In this article, we study the quartic Diophantine equation x4 + y4 – 2z4 – 2w4 = 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.

### Keywords

• Diophantine equation
• Congruent elliptic curve

• 11G05

### References

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## Cite this paper

Moody, D., & Zargar A. S. (2013). On integer solutions of x4 + y4 – 2z4 – 2w4 = 0. Notes on Number Theory and Discrete Mathematics, 19(1), 37-43.