Ferrari's Identity

$(a^2+2ac-2bc-b^2)^4+(b^2-2ab-2ac-c^2)^4$
$+(c^2+2ab+2bc-a^2)^4=2(a^2+b^2+c^2-ab+ac+bc)^4.$

See also Diophantine Equation--Quartic

References

Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 96-97, 1994.