%0 Journal Article
%T The Diophantine Equation $x^4 + 2 y^4 = z^4 + 4 w^4$---a number of improvements
%A Andreas-Stephan Elsenhans
%A J£¿rg Jahnel
%J Mathematics
%D 2010
%I arXiv
%X The quadruple $(1\,484\,801, 1\,203\,120, 1\,169\,407, 1\,157\,520)$ already known is essentially the only non-trivial solution of the Diophantine equation $x^4 + 2 y^4 = z^4 + 4 w^4$ for $|x|$, $|y|$, $|z|$, and $|w|$ up to one hundred million. We describe the algorithm we used in order to establish this result, thereby explaining a number of improvements to our original approach.
%U http://arxiv.org/abs/1006.1196v1