The domain of the function f(x)=\arcsin \left(\log _{m}(n x)\right) 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 .
The domain of the function f(x)=\arcsin \left(\log _{m}(n x)\right) 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 .