Section 4.4 1. Prove that for all integers a, b, , and d, if a|c and b|d then ab|ed. 2. For each of the following statements, determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counterexample if it is false. i. The sum of any three consecutive integers is divisible by 3. ii. For all integers a, b, and , if a|b and a|e, then a|(3b 5). iii. For all integers a, b, and , if a is a factor of and b is a factor of then ab is a factor of . iv. For all integers a, b. and , if ab|c then a|c and blc. v. For all integers a, b, and , if a|(b + ) then alb or alc. vi. For all integers a, b, and , if a|bc then a|b or alc