1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Math proof

  1. Mar 9, 2008 #1
    1. The problem statement, all variables and given/known data

    prove:6 divides (n^3-n) for all integers n.

    2. Relevant equations
    n^3-n=(n)(n+1)(n-1)


    3. The attempt at a solution
    tried to use direct proof. Then used cases that involed n=2k for some integer k and n=2k+1 for some integer k. However, i could not get it so that 6 was factored from either odd/even of n^3-n i.e. n^3-n=6m for some integer m.
    Just a hint please.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 10, 2008 #2
    What's the remainder on division by 3 of the 3 factors you have exhibited?
     
  4. Mar 10, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    One of any two consecutive number is even. One of any three consecutive numbers is a multiple of 3.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Math proof
  1. Math Proof (Replies: 10)

  2. Discrete Math Proof (Replies: 2)

  3. Discrete Math Proof (Replies: 4)

  4. Math Proofs: Relations (Replies: 4)

Loading...