let d=(a,b) then a|bc if and only if a/d is a divisor of c

Question

prove it if it is correct or give counterexample if it is false

let d=(a,b) then a|bc if and only if a/d is a divisor of c

Answer 1

As this is clearly a homework problem, I'm going to give you some hints on how to start instead of spelling out the entire proof.  First, note that if a | bc, then a/d | (b/d)c.  Also note that since d = (a,b), then (a/d) and (b/d) are relatively prime.

 

That should give you enough of a hint to figure out the rest of the proof.  If you still have questions, please let me know.