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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|
|Pages:||pp. 37 - 43|
|Keywords:||Diophantine equation, congruent elliptic curve|
|PDF version:||Click here to retrieve PDF version of paper (282KB)|