Answer
All points one mile from the South Pole and the North Pole.
Work Step by Step
Moving one mile south, if one mile from the South Pole, will put you at the South Pole. Therefore, moving one mile east will not affect your position. Moving north would bring you back where you started.
Moving one mile south, if on the North Pole, would put you one mile south of the North Pole. Moving east does not matter as you will end up at the North Pole after moving one mile north.
