Strings a1,a2,...,a2016 and b1,b2,...,b2016 each contain all natural numbers from 1 to 2016 exactly once each (in other words, they are both permutations of the numbers 1,2,...,2016). Prove that different indices i and j can be found such that aibi−ajbj is divisible by 2017. combinatoricsnumber theorydividesdivisible