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Al(bc), then either alb or alc

  1. Dec 2, 2008 #1
    1. The problem statement, all variables and given/known data
    al(bc), then either alb or alc
    I'm trying to explain why this is true.


    2. Relevant equations



    3. The attempt at a solution
    a divides bc.
    a divides b or a divides c is true because b is just a multiple of c and a will still be a factor.
     
  2. jcsd
  3. Dec 2, 2008 #2
    This statement is true only if a is prime. Use the fact that if gcd (a,b) = c then there is some integers x,y such that ax+by=c
     
  4. Dec 2, 2008 #3

    Mark44

    Staff: Mentor

    It's not true. Counterexample: 4 | 12, but 4 doesn't divide 6 and 4 doesn't divide 2.
     
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