[QUE/CM-05009]

 For a particle moving in Coulomb potential $V(r) = k/r$ show that  the Runge Lenz vector  $$ \vec{N} = \vec{v}\times\vec{L} - k \vec{r}/r  $$   is a constant of motion where $\vec{v}$ is the velocity, and $\vec{L}$  is the angular momentum of the particle