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!

Can you see a counter example that i can't, divisibility problem

  1. Sep 19, 2006 #1
    HEllo everyone. I'm trying to find a counter example that will prove this false. But it may be true but i'm hoping it isn't :)

    For all integers a and b, if a|10b then a|10 or a|b. I said false, a = 3, b = 5. 3 is not divisible by 50. 3 is also not divisble by 10 nor 3 divisible by 5. But then i saw, p has to be true for q to be true. I have to prove q to be false, then p is also false. Its looking like this has to be true, can anyone spot a counter example? I"m not looking for an answer, but it would motivate me to keep looking for one.

    THanks!
     
  2. jcsd
  3. Sep 19, 2006 #2

    0rthodontist

    User Avatar
    Science Advisor

    Try having a > 10 and a > b
     
  4. Sep 20, 2006 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    So we're starting with

    prove or disprove that for all a,b if a|10b then a|10 or a|b.

    A disproof does require one counter example. However, why did you pick a=3 and b=5, since we need to have a|10b and a doesn't divide 10 or b for a counter example, and 3 does not divide 50.

    Hint: p is *prime* if and only if for all m,n p|mn implies p|m or p|n. (so of course a counter example exists, and can be found just by thinking about prime factorizations.
     
  5. Sep 20, 2006 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The question would not be whether 3 is divisible by 50 but whether 50 is divisible by 3. a| 10b means "a divides 10b". I.e. "10b is divisible by a". In any case, the statement says "If a|10b" so you cannot choose an example in which that is not true.
    Well, I don't know because you didn't tell us what p and q are!
    I hope you mean you are not asking for an answer. You certainly should be looking for one! Try this: pick b to be anything you like and pick a to be the biggest number you can find that will divide 10b.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?