f:x-& gt； X 3 is injective in a group, because the order cannot be divisible by 3, so the order of any element cannot be divisible by 3, so the original image of 1 is only 1. Because it is an injective automorphism, it is also injective, that is, all N 3 are completely different in module P, that is, it is a complete system.
The proof skill here is group theory, and you can refer to some other books on group theory.