The Diophantine Equation $x^4+2y^4=z^4+4w^4$---a number of improvements

Andreas-Stephan Elsenhans, Jörg Jahnel

The quadruple $(1484801,1203120,1169407,1157520)$ already known is essentially the only non-trivial solution of the Diophantine equation $x^4 + 2 y^4 = z^4 + 4 w…