n bags with 1 bean, n bags with 3 beans, ..., n bags with 2006 beans
Source: Portugal OPM 2006 p3
May 19, 2024
combinatorics
Problem Statement
A bean packing plant has a machine that puts a certain amount of beans into bags and then puts a certain amount of bags into boxes, which are then shipped to customers. One day, the machine broke down and the first n bags came out empty, the next bags came out with bean, the next bags came out with beans,..., and the last bags came out with beans. To provide each customer with the agreed quantity of bags of beans, the person responsible for the unit intends to distribute the bags among the boxes that day so that all boxes contain the same number of bags and all boxes contain the same number. number of beans. For what values of is this possible?