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Homework Help: Proof by Contradiction || Prove that an equation can never be a square number

  1. Sep 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that for any integer n n^2+n+1, can never be a square number.

    2. Relevant equations

    3. The attempt at a solution
    We could put the equation to a^2, (where a^2 is a square number) and solve for n and show that n can not be an integer.
    I tried quadratic formula on the equation but the solution gets too messy, and i cant prove that the answer is not an integer.
    There must be an easier way to solve this. Just point me in the right direction.
  2. jcsd
  3. Sep 9, 2012 #2


    User Avatar
    Homework Helper
    Gold Member

    That's going to be very hard to prove, as it isn't true: (-1)2+(-1)+1=1=(1)^2
  4. Sep 9, 2012 #3
    Sorry, the question was "for any positive integer n", how do i edit the thread?
  5. Sep 9, 2012 #4
    There should just be a button that says edit in the bottom right of your post.
  6. Sep 9, 2012 #5
    You can't edit your posts after 700 minutes.
  7. Sep 10, 2012 #6
    Problem Solved, close this thread.
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