Let m boxes be given, with some balls in each box. Let n<m be a given integer. The following operation is performed: choose n of the boxes and put 1 ball in each of them. Prove:(a) If m and n are relatively prime, then it is possible, by performing the operation a finite number of times, to arrive at the situation that all the boxes contain an equal number of balls.(b) If m and n are not relatively prime, there exist initial distributions of balls in the boxes such that an equal distribution is not possible to achieve. algorithmrelatively primemodular arithmeticcombinatoricsinvariantIMO Shortlist