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

  • Thread starter haxan7
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  • #1
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Homework Statement



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


Homework Equations


None.


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.
 

Answers and Replies

  • #2
gabbagabbahey
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Homework Statement



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

That's going to be very hard to prove, as it isn't true: (-1)2+(-1)+1=1=(1)^2
 
  • #3
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That's going to be very hard to prove, as it isn't true: (-1)2+(-1)+1=1=(1)^2

Sorry, the question was "for any positive integer n", how do i edit the thread?
 
  • #4
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There should just be a button that says edit in the bottom right of your post.
 
  • #5
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There should just be a button that says edit in the bottom right of your post.

You can't edit your posts after 700 minutes.
 
  • #6
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Problem Solved, close this thread.
 

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