2004 AIME I Problem 8

Define a regular n-pointed star to be the union of n line segments P_1P_2, P_2P_3,\ldots, P_nP_1 such that

- the points P_1, P_2,\ldots, P_n are coplanar and no three of them are collinear,

- each of the n line segments intersects at least one of the other line segments at a point other than an endpoint,

- all of the angles at P_1, P_2,\ldots, P_n are congruent,

- all of the n line segments P_1P_2, P_2P_3,\ldots, P_nP_1 are congruent, and

- the path P_1P_2, P_2P_3,\ldots, P_nP_1 turns counterclockwise at an angle of less than 180 degrees at each vertex.

There are no regular 3-pointed, 4-pointed, or 6-pointed stars. All regular 5-pointed stars are similar, but there are two non-similar regular 7-pointed stars. How many non-similar regular 1000-pointed stars are there?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.