Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By greg1313

Thread: Divisibility problem.

  1. #1
    Newbie
    Joined
    Nov 2017
    From
    Romania
    Posts
    1

    Divisibility problem.

    Prove n(n+4)(n+5) is divisible by 6.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,459
    Thanks
    2728
    Awards
    1

    Re: Divisibility problem.

    Quote Originally Posted by louis33 View Post
    Prove n(n+4)(n+5) is divisible by 6.
    Use induction. If $N(N+4)(N+5)$ is divisible by $6$ then it is plainly obvious so is $(N+1)(N+1+4)(N+1+5)$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2010
    Posts
    2,971
    Thanks
    1141

    Re: Divisibility problem.

    One of $N+4$ and $N+5$ is divisible by 2 (one is odd, the other even).
    One of:
    $N$
    $N+4 = (N+1)+3$
    $N+5 = (N+2)+3$
    is divisible by 3 (the other two are not).

    Any product that is divisible by both 2 and 3 is divisible by 6.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,695
    Thanks
    318

    Re: Divisibility problem.

    Quote Originally Posted by louis33 View Post
    Prove n(n+4)(n+5) is divisible by 6.
    n must be an integer, of course...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Dec 2016
    From
    Earth
    Posts
    141
    Thanks
    59

    Re: Divisibility problem.

    Quote Originally Posted by louis33 View Post
    Prove n(n+4)(n+5) is divisible by 6.
    n(n + 4)(n + 5) =

    n^3 + 9n^2 + 20n =

    n^3 + 3n^2 + 2n + 6n^2 + 18n =

    n(n + 1)(n + 2) + 6(n^2 + 3n)
    Thanks from JeffM
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Divisibility Problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Jul 11th 2014, 02:25 AM
  2. Divisibility problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 26th 2012, 03:15 AM
  3. [SOLVED] Divisibility Problem
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: Jun 28th 2011, 08:53 AM
  4. problem with divisibility
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: Sep 8th 2010, 09:06 AM
  5. A divisibility problem
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: Aug 19th 2010, 09:21 PM

/mathhelpforum @mathhelpforum