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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

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    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

    Gokul43201

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    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

    Zurtex

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    Bah, I was just about to put the exact same counter example up :wink:
     
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