(d): We have worked out that the statement holds if and only if p divides 2b. To disprove, we need a counterexample. First, let a+c be a prime number, say a+c=13 which is only divisible by 1 and itself. Second, choose any 1
(e): Work it out case by case and you should see that the statement is true.

(f): Notice that one shortcut is to use results from (e).

Do clarify if you have any further questions.