Let N particles interact according to $$ma\frac{d^2xa^i}{dt^2}=-\frac{\partial V(x)}{\partial xa^i}$$ with $a=1,...,N$. Suppose $V(x1,...,xN)$ depends only on the differences $xa^i-xb^i$, with $a,b=1,...,N$. Show that the total momentum $\suma ma \frac{dxa^i}{dt}$ is conserved.