When writing a proof statement in math, what's the best way to disprove a, b, and c as positive integers?

I understand the idea of how to disprove, but I want to know how one would try to disprove the following statement:





If a, b, and c are positive integers with a|(bc), then a|b or a|c

When writing a proof statement in math, what's the best way to disprove a, b, and c as positive integers?
a|(bc) =%26gt; a|b or a|c is true for some choices of a, b, and c (e.g. trivially if a = 1), so you can't disprove it for general a, b, and c.





But the statement you're asked to disprove is stronger -- it asserts this condition for all positive a, b, and c. Therefore, you want to disprove the "all" part, by showing a choice for a, b, and c such that a|(bc) but a|b and a|c are false.





If you're having trouble, think about the case a = bc, which guarantees a|(bc).
Reply:Find a counterexample. Three specific integers a, b, and c where the statement is false. Namely find three specific numbers a, b, and c where a|(bc) but a does not divide either b or c. So a divides the product without dividing either of the factors.





Should not take you long to come up with some examples,