Hello everybody!

A problem:

Find functions $\displaystyle \varphi , \psi $ which are fulfilling:

$\displaystyle \varphi(x^2+y^2)=\psi(x) \psi(y) $ for all $\displaystyle x,y$.

Prove that if $\displaystyle \varphi , \psi $ are fulfilling the above equation then $\displaystyle \psi $ determined by $\displaystyle \varphi $. How?

Thank you.