True or false division algorithm problem

Let a,b,c be integers with a not equal to 0 and (b,c)=1. If a divides the product of bc, then a must divide b or a must divide c.

My thoughts: I can prove this if (a,b)=1. but I believe it is false because I cannot prove that that b/a or c/a is an integer.

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Can you please share your thoughts on the problem, and explain what you've tried? This will help people write responses that are relevant to your question. (Also, this has surely been asked before on this site.) –  T. Bongers Jan 25 at 4:01
hasnt been answered before. not this exact type –  D-Man Jan 25 at 4:05
False, take $a=6$, $b=2$ and $c=3$.
Hint $\$ Let $\ a = bc,\ \ b,c > 1$