Results 1 to 7 of 7

Math Help - Division

  1. #1
    Member
    Joined
    Feb 2008
    Posts
    79

    Division

    This is just a confirmation of the work I have done:

    Indicate if the following are true or false. If false, give a counterexample:

    1.) If b|(a+b), then d|a or d|b

    False: 3|(7+2), but 3 does NOT | 7 or 3 does NOT | 2

    2.) If ab|c, a =! 0 and b =! 0, then a|c and b|c

    True

    3.) If d|a and d|b, then d|(ax + by) for all integers x and y

    True

    4.) If d|a^2, then d|a

    True
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2008
    Posts
    147
    4.) false
    Take a = 6, then a^2 = 12. 4|12, but not 6.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2008
    Posts
    79
    Quote Originally Posted by terr13 View Post
    4.) false
    Take a = 6, then a^2 = 12. 4|12, but not 6.
    Uh, 6^2 = 36, not 12.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2008
    Posts
    147
    Wow, I'm bad at math. Take a=4, then a^2= 16. 8|16, but 8 does not divide 4.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    1.) If b|(a+b), then d|a or d|b

    False: 3|(7+2), but 3 does NOT | 7 or 3 does NOT | 2



    2.) If ab|c, a =! 0 and b =! 0, then a|c and b|c

    True



    3.) If d|a and d|b, then d|(ax + by) for all integers x and y

    True



    4.) If d|a^2, then d|a

    True

    Look at terr13's example
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2008
    Posts
    11
    Quote Originally Posted by DiscreteW View Post
    4.) If d|a^2, then d|a

    True
    this is not true unless d is a prime number
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Oct 2008
    Posts
    147
    That is essentially the definition of a prime element, if a is prime and a|bc, then a|b or a|c.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Division
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 18th 2010, 11:50 AM
  2. Polynomial division vs synthetic division
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 9th 2009, 05:49 AM
  3. division
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: November 16th 2008, 09:57 PM
  4. division
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 13th 2008, 06:05 PM
  5. division
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 8th 2007, 11:41 AM

Search Tags


/mathhelpforum @mathhelpforum