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Prove that 3n^2 - 1 can't be a square of a integer n

  1. Jan 31, 2009 #1
    Well, the problem statement is in the title:
    Given that n is an integer, show that 3n2 - 1 can't be the square of an integer.

    Currently, I don't have any idea at all where to start. Method is probably to assume opposite and show that this leads to a contradiction.

    Any hint as to where to start would be very appreciated!
     
  2. jcsd
  3. Jan 31, 2009 #2

    Dick

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    Look at remainders mod 4. What are the possible values for n^2 mod 4?
     
  4. Feb 1, 2009 #3
    Thanks for the reply!

    While that probably is one way of looking at the problem, we haven't yet reached modulus in our studies.
     
  5. Feb 1, 2009 #4

    Dick

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    You don't really need to study modulus to think about remainders after division by 4. Nothing else comes to mind as an approach.
     
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