Results 1 to 2 of 2

Thread: Proove that...

  1. #1
    Newbie Sorombo's Avatar
    Joined
    Feb 2011
    Posts
    13

    Proove that...

    Proove that for every $\displaystyle $n \in \mathbb{N}$$

    $\displaystyle n^3-9n+27\not\equiv 0 \mod 81$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5

    Re: Proove that...

    Quote Originally Posted by Sorombo View Post
    Proove that for every $\displaystyle $n \in \mathbb{N}$$

    $\displaystyle n^3-9n+27\not\equiv 0 \mod 81$
    Suppose otherwise, then there exists a $\displaystyle k\in \mathbb{Z}$ such that:

    $\displaystyle n^3-9n+27=k\times 81=k\times 9^2$

    which implies that $\displaystyle 9|n^3$ which in turn implies that $\displaystyle 3|n$.

    Hence there exists a $\displaystyle \lambda \in \mathbb{N}$ such that:

    $\displaystyle 27 \lambda^3-27 \lambda +27=3 \times k \times 27$

    or:

    $\displaystyle \lambda^3- \lambda +1=3 \times k$

    Now consider the left hand side modulo 3.

    CB
    Last edited by CaptainBlack; Sep 20th 2011 at 11:26 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How can I proove this?
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Sep 22nd 2010, 05:36 AM
  2. How do I proove this
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Jun 8th 2010, 05:47 PM
  3. Proove
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 7th 2009, 10:59 PM
  4. Proove by Induction
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Mar 22nd 2009, 10:50 AM
  5. Proove this identity
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Jun 23rd 2008, 08:37 AM

Search Tags


/mathhelpforum @mathhelpforum