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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.
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 October 10, 2025)