Let R be the set of all possible remainders when a number of the form 2^{n}, n a nonnegative integer, is divided by 1000 . Let S be the sum of the elements in R. Find the remainder when S is divided by 1000.
Let R be the set of all possible remainders when a number of the form 2^{n}, n a nonnegative integer, is divided by 1000 . Let S be the sum of the elements in R. Find the remainder when S is divided by 1000.