Carmichael's Identity

(m^2 - n^2 - p^2 + q^2)^2 + (2nm - 2pq)^2 + (2mp + 2nq)^2

= (m^2 + n^2 + p^2 + q^2)^2


http://www.cut-the-knot.org/wiki-math/index.php?n=Algebra.CarmichaelsIdentity