1. Limited time only! Sign up for a free 30min personal 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!

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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook