Question 5
For distinct positive integers $a,b\lt 2012$, let $f(a,b)$ count the integers $1\le k\lt 2012$ for which the remainder of $ak$ modulo 2012 exceeds that of $bk$. Determine the minimum $S$ over all such pairs $(a,b)$.
Proposed by Warut Suksompong (credit in the supplied notes).
Proposed by Warut Suksompong (credit in the supplied notes).