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Proof - If the square of an integer is even, . . .

  1. Apr 7, 2009 #1
    Hi,
    I have no idea on how to start to do this question.
    If the square of an integer is even,then the integer itself is even

    I try to check some books but i can't get any similar examples.I wonder if I can directly prove the n=2k, n^2 = 2(2k^2).

    Thanks!
     
  2. jcsd
  3. Apr 7, 2009 #2

    matt grime

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    Re: proof

    But that is the converse of what you were asked to show. You want to show that if m^2 is even, then m is even. One of the definitions of a prime number makes this instantaneous. What definitions of prime do you know?

    Alternatively you can show that if n is odd, then n^2 is odd.
     
  4. Apr 7, 2009 #3

    tiny-tim

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    Welcome to PF!

    Hi yanjt! Welcome to PF! :smile:

    Try proving it the other way round:

    if an integer is odd, its square is odd. :wink:
     
  5. Apr 7, 2009 #4
    Re: proof

    Prime number is number that can be divided by or itself.
    if i prove that an integer is odd,its square is odd,I am not using contradiction to prove it,right?I can show that if an integer is odd,its square is odd.Yet, how can i show that if the square of an integer is even,the integer itself is even?

    Thanks for ur help!

    p/s:Thanks tiny-tim!I found this website is really useful!=)
     
  6. Apr 7, 2009 #5

    matt grime

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    Re: proof

    What's wrong with using proof by contradiction?
     
  7. Apr 8, 2009 #6
    Re: proof

    Nothing is wrong using contradiction.What i mean is that,i wonder if proof "if n is odd,n^2 is odd" is a kind of contradiction?
     
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