Results 1 to 2 of 2

Math Help - Divisibility by 9

  1. #1
    Junior Member CuriosityCabinet's Avatar
    Joined
    Aug 2010
    From
    UK
    Posts
    32
    Thanks
    1

    Divisibility by 9

    Prove that, for any positive integer n

    n(n-1)(n-2) - 6 \begin{bmatrix} \frac{n}{3} \end{bmatrix}

    is divisible by 9.

    \begin{bmatrix} x \end{bmatrix} denotes the integer part of x.

    I wasn't sure how to go about this question, any help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by CuriosityCabinet View Post
    Prove that, for any positive integer n

    n(n-1)(n-2) - 6 \begin{bmatrix} \frac{n}{3} \end{bmatrix}

    is divisible by 9.

    \begin{bmatrix} x \end{bmatrix} denotes the integer part of x.

    I wasn't sure how to go about this question, any help?
    There are various methods you can try. How about using induction? Another way is to solve it on a case by case analysis. Prove it for the three cases n = 3k, n = 3k +1 and n = 3k + 2. The latter method gets rid of the greatest integer function and makes the solution pretty clear
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Divisibility 11
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: December 20th 2008, 02:41 AM
  2. Divisibility (gcd) 10
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 19th 2008, 04:44 PM
  3. Divisibility (gcd) 9
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 19th 2008, 01:12 PM
  4. Divisibility (gcd) 8
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: December 19th 2008, 03:53 AM
  5. Divisibility
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 14th 2008, 09:24 AM

Search Tags


/mathhelpforum @mathhelpforum