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Math Help - If a, b, c ∈ Z+ and a|bc, does it follow that a|b or a|c?

  1. #1
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    If a, b, c ∈ Z+ and a|bc, does it follow that a|b or a|c?

    If a, b, c ∈ Z+ and a|bc, does it follow that a|b or a|c?

    I don't believe it follows either because from what I have learned :

    ([a|b ^ b|c)]→a|c
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  2. #2
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    Re: If a, b, c ∈ Z+ and a|bc, does it follow that a|b or a|c?

    Quote Originally Posted by mizzlizzym View Post
    If a, b, c ∈ Z+ and a|bc, does it follow that a|b or a|c?
    I don't believe it follows either because from what I have learned :

    Well 6|(3\cdot 4) but ?
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    Re: If a, b, c ∈ Z+ and a|bc, does it follow that a|b or a|c?

    If a prime p|ab then either p|a or p|b

    If a|bc and a and b are relatively prime, the a|c.
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