Results 1 to 2 of 2

Thread: divisibility proof

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    20

    divisibility proof

    The question I am working on is
    Prove that a/b if and only if a^3/b^3.

    I know that if p/a^n then p/a...but how can i apply that here..can i make a prime on my own despite the question did not say?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by empressA View Post
    The question I am working on is
    Prove that a/b if and only if a^3/b^3.

    I know that if p/a^n then p/a...but how can i apply that here..can i make a prime on my own despite the question did not say?
    I'm pretty sure we can go through with bi-implications this way.

    $\displaystyle a|b \Leftrightarrow b = ka$ for some $\displaystyle k \in \mathbb Z$

    $\displaystyle \Leftrightarrow b^3 = k^3a^3$

    $\displaystyle \Leftrightarrow a^3|b^3$ since $\displaystyle k \in \mathbb Z \implies k^3 \in \mathbb Z$

    and done.


    Now if that makes you uncomfortable, and you want to do both directions, change all the above $\displaystyle \Leftrightarrow$'s to $\displaystyle \implies$'s and consider that your proof of the forward direction.

    For the backwards direction, you will need to work a little harder. Personally, I'd do a proof by contradiction, employing the division algorithm.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Divisibility proof
    Posted in the Algebra Forum
    Replies: 7
    Last Post: Jun 10th 2010, 10:47 AM
  2. Divisibility Proof
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: Mar 16th 2009, 06:11 PM
  3. divisibility proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Jan 20th 2009, 10:27 PM
  4. Proof of divisibility
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Oct 13th 2008, 01:53 PM
  5. Divisibility proof
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Sep 10th 2008, 07:07 AM

Search Tags


/mathhelpforum @mathhelpforum