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If a divides bc, then a divides b or a divides c

  1. Jun 11, 2010 #1
    If [tex]a|bc[/tex], then [tex]a|b[/tex] or [tex]a|c[/tex].

    [tex]a|bc\Leftrightarrow am=bc\Leftrightarrow a\left(\frac{m}{b}\right)=c[/tex]

    Hence, [tex]a|c[/tex]
  2. jcsd
  3. Jun 11, 2010 #2


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    That statement is false as stated. Let b = 6, c = 10. Then a = 4 divides bc = 60 but a doesn't divide either b or c.
  4. Jun 12, 2010 #3
    Your proof is false because you are dividing by b. This is incorrect since b could be 0.
    Last edited: Jun 12, 2010
  5. Jun 12, 2010 #4
    he also doesn't know whether m/b will be an integer or not.

    I am guessing you are reading an introductory number theory book. you should refrain from dividing as much as possible in your proofs. modding out is acceptable later when you start doing it, but don't divide unless you know that the denominator is NOT zero and the quotient is an integer.
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