If the following statement is false, provide a counterexample; if the following statement is true, write a proof: "For all integers a,b, and c if a|bc then a|b or a|c".

Answer 1

The statement is false. We can find a counterexample: Let a=4, b=6, and c=10. It is clear that 4|(6*10). But 4 doesn't divide 6 and 4 doesn't divide 10.