Problems(1)
For distinct positive integers a,b<2012, define f(a,b) to be the number of integers k with 1≤k<2012 such that the remainder when ak divided by 2012 is greater than that of bk divided by 2012. Let S be the minimum value of f(a,b), where a and b range over all pairs of distinct positive integers less than 2012. Determine S. 2012 USAJMO