MathDB

3

Part of 2006 Portugal MO

Problems(1)

n bags with 1 bean, n bags with 3 beans, ..., n bags with 2006 beans

Source: Portugal OPM 2006 p3

5/19/2024
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 nn bags came out with 11 bean, the next nn bags came out with 22 beans,..., and the last nn bags came out with 20062006 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 20072007 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 nn is this possible?
combinatorics