Homomorphism and Monomodrphism

Question

The number of homomorphism from " group of integers under addition modulo n" to "group of integers under addition"1 i.e from Zn to (Z,+) is 1. So it must be trivial homomorphism. I want to ask total number of injective homomorphism (i.e monomorphism) from Zn to (Z,+) group ? I can understand if n =2 or n >2 then we get zero monomorphism . But what about n =1 ? Where n = order of group Zn.