Perfect difference sets and Sidon sets

Consider a wheel with 21 evenly spaced positions, consecutively numbered 0, 1, 2, up to 20, and highlight the positions 1, 2, 5, 15, and 17 in bold, as in the picture. Can we find two marked positions that are one tick of the circle apart? Yes: 1 and 2. How about two marked positions that are two ticks apart? Yes: 15 and 17. Three ticks apart? Yes: 2 an…