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Homework Help: Is there an easier way

  1. Oct 13, 2008 #1
    Last edited by a moderator: Apr 23, 2017
  2. jcsd
  3. Oct 13, 2008 #2
    Re: Is there an easier way....

    Well, consider the sets of integers (1,...,n) (n+1,...,2n) and so on (and the negatives likewise). Now, these partition the integers. Take n consecutive integers anywhere in the integers and for none of them to divide n exactly you would have to fit them inside one of these sets. That's impossible of course. For two to divide n, you would have to overlap mn and (m+1)n for some integer m. That's also impossible without at least n+1 integers. QED.
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