IMO 1970 LL NET33

Origin: NET

Problem

The vertices of a given square are clockwise lettered A, B, C, D. On the side AB is situated a point E such that AE = AB/3. Starting from an arbitrarily chosen point P0 on segment AE and go- ing clockwise around the perimeter of the square, a series of points P0, P1, P2, . . . is marked on the perimeter such that PiPi+1 = AB/3 for each i. It will be clear that when P0 is chosen in A or in E, then some Pi will coincide with P0. Does this possibly also happen if P0 is chosen otherwise?