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Publication Citation: On integer solutions of x^4+y^4-2z^4-2w^4=0

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Author(s): Dustin Moody; Arman S. Zargar;
Title: On integer solutions of x^4+y^4-2z^4-2w^4=0
Published: September 18, 2013
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
Pages: pp. 37 - 43
Keywords: Diophantine equation, congruent elliptic curve
Research Areas: Math
PDF version: PDF Document Click here to retrieve PDF version of paper (282KB)