Function on Integers

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  • #1
playa007
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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.

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The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
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Good question. But the rules of the forum say you have to at least try to find a solution before anyone can help.
 
  • #3
playa007
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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,...
 
  • #4
Dick
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What happens if n=1? Then think about n=2.
 
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