Statement

After graduation, Marco gave a party to celebrate in style the end of his studies! As in every respectable party, he brought a lot of confetti of different types for his guests. The party is now over and Marco realized that he still has plenty of leftover confetti! He has already eaten lots of them and does not want to exaggerate, thus he had come up with a nice idea. He wants to distribute confetti to his friends but being careful not to make anyone unhappy. In fact, he has C_0 confetti of one type, C_1 confetti of another type and so on… for a total of N different types. Marco wants to invite some friends and give the same quantity of confetti to all of them and this must hold for all the types of confetti. He also does not want to keep any for himself: if there are four confetti of a given type, he can invite only one, two or four friends to make a fair division. Help him: how many friends can he invite?