Snail, you are the one who claims maths proficiency. n=5 works, the cases of n up to 4 can be tested manually or by a little computer script. My friend was not too specific in his email.

Little # games? Questions of the type "is this true for all integers?" are often easy to ask and difficult to answer with a proof. This one turned out to be of medium difficulty, others like Fermat's theorem took centuries to be answered by professional mathematical researchers. Football is a little ball game, but we might not enjoy playing it against Bayern München or Real Madrid if we seriously want to win.