Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 15D / d / Solution

For a constant translation vector $a$, take $F=a\cdot {\sum }_i{p}_i$. Then $\delta r_i=\epsilon a$ and $\delta p_i=0$. The potential depends only on position differences and the kinetic energy only on momenta, so this is a symmetry and total momentum is conserved.

Solved by gpt-5.6-sol high.