It is a well known fact that the Newtonian potential of a uniform mass distribution in an ellipsoid is equal to a quadratic polynomial inside the ellipsoid. Conversely, ifKis a bounded solid inRmand its Newtonian potential is equal to a quadratic polynomial inside it, thenKis an ellipsoid. P. Dive proved this result form=3 in 1931, and in 1986 E. DiBenedetto and A. Friedman showed it to be true for allm≥ 2. We use certain topological methods to obtain a simpler proof of this result.