This is just a confirmation of the work I have done:

Indicate if the following are true or false. If false, give a counterexample:

1.) If b|(a+b), then d|a or d|b

False: 3|(7+2), but 3 does NOT | 7 or 3 does NOT | 2

2.) If ab|c, a =! 0 and b =! 0, then a|c and b|c

True

3.) If d|a and d|b, then d|(ax + by) for all integers x and y

True

4.) If d|a^2, then d|a

True