Non-Bijective Function from Integers to Integers

[playa007]

Homework Statement

Is it possible to find a non-bijective function from the integers to the integers such that:
f(j+n)=f(j)+n where n is a fixed integer greater than or equal to 1 and j arbitrary integer.

Homework Equations

The Attempt at a Solution

 

[Dick]

Good question. But the rules of the forum say you have to at least try to find a solution before anyone can help.

 

[playa007]

I haven't considered the possibility that the condition f(j+n)=f(j)+n forces bijectivity. But clearly the condition implies a bunch of things would not work: nothing of the form f(j)=mj where m>1, floor/ceiling functions, any functions which are constant between two integers,...

 

[Dick]

What happens if n=1? Then think about n=2.