In Venetiania, the smallest currency is the ducat. The finance minister instructs his officials as follows: "I wish six kinds of banknotes, each worth a whole number of ducats. Those six values must be such that there exists a number N with the following property:
Any amount of money of n ducats (n positive and integer) where n≤N may be paid in such a way that no more than two copies of each kind are required either to pay or to return. I also wish those six values to be as large as possible for N. Determine those six values and provide proof that all conditions have been met."
Solve the problem of those officials combinatoricsnumber theory