Show that the identity mapping is the only ring homomorphism fromZintoZ.

I know that:

Ring homomorphism exsits if there is a function φ: RàS such that the following are true:

i) φ(a+b) = φ(a) + φ(b)

ii) φ(ab) = φ(a)φ(b)

iii) φ(1) = 1

Identity mapping maps each element of R to itself, and is always bijective.

I need help writing the proof of this. Thanks ahead of time.