We prove that arbitrary (nonpolynomial) scalar evolution equations of order $m\ge 7$, that are integrable in the sense of admitting the canonical conserved densities $\ro^{ (1)}$, $\ro^{ (2)}$, and $\ro^{ (3)}$ introduced in [MSS,1991], are polynomial in the derivatives $u_{ m-i}$ for $i=0,1,2.$ We also introduce a grading in the algebra of polynomials in $u_k$ with $k\ge m-2$ over the ring of functions in $x,t,u,...,u_{ m-3}$ and show that integrable equations are scale homogeneous with respect to this grading.
Categories: nlin.SI