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

1. 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

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

Originally Posted by mizzlizzym
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 ?

3. 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.