1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is there an easier way

  1. Oct 13, 2008 #1
    Is there an easier way....

    to prove this?

    I did a proof by cases.
     
  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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Is there an easier way
Loading...