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Function on Integers

  1. Sep 19, 2012 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 19, 2012 #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.
     
  4. Sep 19, 2012 #3
    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,...
     
  5. Sep 19, 2012 #4

    Dick

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    What happens if n=1? Then think about n=2.
     
    Last edited: Sep 19, 2012
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