Ah, missed the N... But more interestingly, the non-negative integers 0...p-1 modulo a prime number p form a field (where -1, -2 etc. appear in a natural way),

Ah, missed the N... But more interestingly, the non-negative integers 0...p-1 modulo a prime number p form a field (where -1, -2 etc. appear in a natural way), and so their tuples of some fixed length do form a vector space.