  No Runge-Kutta method can be energy preserving for all Hamiltonian systems.
But for problems in which the Hamiltonian is a polynomial, the Averaged Vector
Field (AVF) method can be interpreted as a Runge-Kutta method whose weights
$b_i$ and abscissae $c_i$ represent a quadrature rule of degree at least that
of the Hamiltonian. We prove that when the number of stages is minimal, the
Runge-Kutta scheme must in fact be identical to the AVF scheme.
