4.) false
Take a = 6, then a^2 = 12. 4|12, but not 6.
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
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
Look at terr13's example