1997 AIME Problem 6

Point B is in the exterior of the regular n-sided polygon A_1A_2\cdots A_n, and A_1A_2B is an equilateral triangle. What is the largest value of n for which A_1, A_n, and B are consecutive vertices of a regular polygon?

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.