1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Proving Basic Theorem

  1. Sep 11, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove a theorem using direct proof, mathematical induction, contraposition, or contradiction.

    2. Relevant equations

    "If m divides n, then m <= n."

    3. The attempt at a solution

    (a) Suppose m divides n, then m = nk for some integer k.

    (b) If k = 1, the m = n(1) = n.

    That show equality part. How do I now show inequality? I'm at a loss for the next step.
  2. jcsd
  3. Sep 11, 2007 #2


    User Avatar
    Science Advisor

    If k is not 1, then, since it is a positive integer, k>1. What does that tell you?
  4. Sep 11, 2007 #3
    Given that, for k=1, m = n,

    then for k > 1 (or k + 1),

    m < n(k + 1).

    If I divide by k + 1,

    m / (k + 1) < n.

    Am I on the right track?
    Last edited by a moderator: Sep 11, 2007
  5. Sep 11, 2007 #4
    If m divides n (m<=n), then m*k=n and not m=n*k.

    If k=1, m=n, if k>1,

    mk=n => m<n.
  6. Sep 11, 2007 #5


    User Avatar
    Science Advisor

    You're right! I missed that completely!
  7. Sep 11, 2007 #6
    Sleek, Thanks! I guess I got that twisted. Appreciate your helping me understand this logically.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook