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!

Divisibility property

  1. Jul 31, 2010 #1
    1. The problem statement, all variables and given/known data

    proof the theorem

    if a l b and b l a then a=+-b

    2. Relevant equations



    3. The attempt at a solution

    there exist integer p,q such that ap=b and bq=a, then i've no idea how i can relate it to a=+-b.. clue please T_T
     
  2. jcsd
  3. Jul 31, 2010 #2
    [tex] ap = b = (\frac{a}{q}) [/tex]

    Multiply by q and divide be a (since b|a <--> a is not 0), giving us:

    [tex] pq = 1 [/tex]

    Do you follow?
     
  4. Jul 31, 2010 #3
    yea yah, i thought that too, but don't know to continue from there too, owhoho, more clue please, ;P
     
  5. Jul 31, 2010 #4
    wait, let me think first
     
  6. Jul 31, 2010 #5

    Mark44

    Staff: Mentor

    So b = pa and a = qb, for some integers p and q.
    Then b = pa = p(qb) = (pq)b.

    What can you say about pq?
     
  7. Jul 31, 2010 #6
    Remember, p and q are both nonzero integers.
     
  8. Jul 31, 2010 #7
    hmm, so pq=1 , hence, p=1 and q=1, hence a=b and b=a, still cannot get +-b, T_T
     
  9. Jul 31, 2010 #8
    WAIIITTTT (-1)(-1) also equal 1, wait wait let me think again
     
  10. Jul 31, 2010 #9
    so i get

    a=b or (a=-b and b=-a)

    => (a=b or a=-b) and (a=b or b=-a)

    (a=b or a=-b) is enough to verify it right?
     
  11. Jul 31, 2010 #10
    Yep, though technically you're proving, not verifying. "Proving" is a stronger word...makes you sound "smarter/cooler" :P!
     
  12. Jul 31, 2010 #11
    owho, thankyou very much
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Divisibility property
  1. Divisibility property (Replies: 26)

  2. Polynomial division (Replies: 11)

  3. Induction Division (Replies: 2)

  4. Division algorithm (Replies: 13)

Loading...