Results 1 to 2 of 2

Math Help - Divisibility by 6 Induction

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    86

    Divisibility by 6 Induction

    Hey all, some help finishing this proof would be appreciated:

    For all k in the Naturals, k^3 + 5k is divisible by 6.

    Proof:
    1^3 + 5(1) = 6 which is divisible by 6

    P(n): n^3 +5n = 6y

    (n+1)^3 + 5(n+1) = 6z
    (n^3 + 3n^2 + 3n + 1) + 5(n+1)
    6y + 3n^2 + 3n + 6 = 6z
    3(2y + n^2 + n + 2) = (3*2)z

    where do we go from here? How can I show divisibility by 6 here? Thanks in advance for the help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by jstarks44444 View Post
    Hey all, some help finishing this proof would be appreciated:

    For all k in the Naturals, k^3 + 5k is divisible by 6.

    Proof:
    1^3 + 5(1) = 6 which is divisible by 6

    P(n): n^3 +5n = 6y

    (n+1)^3 + 5(n+1) = 6z
    (n^3 + 3n^2 + 3n + 1) + 5(n+1)
    6y + 3n^2 + 3n + 6 = 6z


    where do we go from here? How can I show divisibility by 6 here? Thanks in advance for the help!
    I deleted your last line above.

    6y+6 is divisible by 6

    3n^2+3n=3n(n+1)

    One of n and n+1 is even.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Induction - Divisibility
    Posted in the Algebra Forum
    Replies: 11
    Last Post: December 24th 2011, 09:04 PM
  2. Induction divisibility P1
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 6th 2010, 11:20 AM
  3. Induction divisibility P2
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 6th 2010, 10:22 AM
  4. Prove divisibility by 7 (using induction)
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 29th 2008, 12:12 PM
  5. Induction with divisibility
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: April 28th 2008, 09:34 AM

Search Tags


/mathhelpforum @mathhelpforum