Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Some more brain exercises!

  1. Jun 20, 2004 #1
    hey i have more problems that can really exercise the mind! here are 3.

    1. prove if q is divisible by (r +s) then either q is divisible by r or q is divisible by s.

    2. if d>0, (fd+ed) = d(f,e). proof.

    3. a divisible by b => a^m divisible by b^m a,b,m are in Z+.

    i think i have some thoughts and i will share.

    1. say that (b+c) = ma, where m is in Z+. after that, i am guessing...

    2. could use contradiction here. say that d=0, then show the proof? anyone has any takes on this?

    3. there exist m and n s.t. bn=ma. lost after here.

    anyone w/ information/thoughts please share.
  2. jcsd
  3. Jun 21, 2004 #2
    For number 3, just apply the definition of "divisibility"... There is a k such that a = bk, and thus a^m = (bk)^m = b^m * k^m, and so a^m / b^m = k^m \in Z, hence b^m | a^m.
  4. Jun 21, 2004 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    what does the notation in 1 mean, are you talking about ideals?

    the second follows, i believe, if you show the RHS divides the LHS and the LHS divides the RHS
  5. Jun 21, 2004 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What does (a+b) denote ?
  6. Jun 25, 2004 #5
    Number 1: By (r+s), do you mean the sum of r and s? If so, a quick counterexample: 25 is divisible by (2+3) but it's not divisible by 2 or by 3.
  7. Jun 25, 2004 #6


    User Avatar
    Science Advisor
    Homework Helper

    Bah, I was just about to put the exact same counter example up :wink:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook