Common Divisor Divides Integer Combination/Corollary/Converse does not Hold

Theorem
Let $a, b, c \in \Z$ be integers.

Let:
 * $c \divides \paren {a + b}$

Then it is not necessarily the case that:
 * $c \divides a \land c \divides b$

Proof
Proof by Counterexample:

Let $a = 2, b = 4, c = 3$.

Then we have:
 * $3 \divides \paren {2 + 4}$

but:
 * $3 \nmid 2$

and:
 * $3 \nmid 4$