[Author] V. S. Kalnitsky [Title] Means generating the cone sections and the third degree polynomials [AMS Subj-class] 39B22 Equations for real functions [Abstract] Here we give the complete characterization of polynomials as a solution of the symmetrical diffrence-functional equation, generalizing the well-known Lagrange equation. The key notion is the conjugation by the linear transformation. [Keywords] generalized means, difference-functional equation [Comments] Main part of the article was reported at Albertina University at Hilbert's readings. English, LaTeX, 6 pp. [Contact e-mail] skalnitsky@hotmail.com