Imagine you have n points evenly spaced around a circle. Choose one of these as the starting point, p0. Take a pen and draw a line skipping m – 1 points so that you connect p0 to pm.
Continue doing this without lifting the pen (so next you connect pm to the point m points later, and so on). Eventually you get back where you started.
Perhaps you have drawn an n-pointed star (the classic way of drawing a 5 pointed start is with n = 5 and m = 2).
Why can you never get a six pointed start this way? What other values of n will never result in a star?