  We show that any homogeneous polynomial solution of |\nabla
F(x)|^2=m^2|x|^(2m-2), m>1, is either a radially symmetric polynomial F(x)=\pm
|x|^m (for even m's) or it is a composition of a Chebychev polynomial and a
Cartan-M\"unzner polynomial.

Analysis of PDEs;Differential Geometry