Results 1 to 4 of 4

Math Help - Prove that n^2 - 1

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    3

    Prove that n^2 - 1

    Hey everyone, I have this problem for homework and got started on it when n is odd (easy). But can't figure out how to solve it when n is even:


    Let n be an integer greater than or equal to 3. Prove that n^2 -1 is not prime.


    So I split it into when n is odd and when n even.

    ODD:

    n = 2c + 1
    n^2 - 1 = (2c + 1)^2 - 1
    "" = 4c^2 + 4c + 1 - 1
    "" = 2(2c^2 + 2c)
    d = 2c^2 + 2c
    "" = 2d

    Therefore 2 | n^2 -1, so n^2 -1 isn't prime for odd numbers

    But I can't figure out where to go from here for even n's. Any hints on how to think about this?
    Last edited by mr fantastic; September 14th 2010 at 03:21 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by dblaisewatson View Post
    Hey everyone, I have this problem for homework and got started on it when n is odd (easy). But can't figure out how to solve it when n is even.



    So I split it into when n is odd and when n even.

    ODD:

    n = 2c + 1
    n^2 - 1 = (2c + 1)^2 - 1
    "" = 4c^2 + 4c + 1 - 1
    "" = 2(2c^2 + 2c)
    d = 2c^2 + 2c
    "" = 2d

    Therefore 2 | n^2 -1, so n^2 -1 isn't prime for odd numbers

    But I can't figure out where to go from here for even n's. Any hints on how to think about this?
    You can handle even and odd at once by factoring n^2 - 1 (think: difference of squares).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    undefined has shown that it needs just one case.

    Following on from your logic....

    n even
    n=2c

    n^2-1=4c^2-1=(2c+1)(2c-1)

    which is the product of two factors, hence non-prime.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2010
    Posts
    3

    Thanks

    Thanks guys. I was making it way more difficult than it had to be, as I so often do
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove that
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: May 21st 2010, 05:48 AM
  2. Prove n^2<= ......
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: November 17th 2009, 05:52 AM
  3. Replies: 2
    Last Post: August 28th 2009, 02:59 AM
  4. prove that
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 7th 2008, 05:14 PM
  5. prove
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 7th 2008, 01:45 PM

Search Tags


/mathhelpforum @mathhelpforum