A Functional Equation Originating from Elliptic Curves

Abstract EN

We obtain the general solution and the stability of the functional equation f(x+y+z,u+v+w)+f(x+y−z,u+v+w)+2f(x,u−w)+2f(y,v−w)=f(x+y,u+w)+f(x+y,v+w)+f(x+z,u+w)+f(x−z,u+v−w)+f(y+z,v+w)+f(y−z,u+v−w).

The function f(x,y)=x3+ax+b−y2 having level curves as elliptic curves is a solution of the above functional equation.