2013 AIME I Problem 8

The domain of the function f(x) = \arcsin(\log_{m}(nx)) is a closed interval of length \frac{1}{2013} , where m and n are positive integers and m>1. Find the remainder when the smallest possible sum m+n is divided by 1000.

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.