Is this statement true or false

I need to determine if the following statement is true or false. If it's false i need to disprove it and if it's true i need to prove it.

Suppose a is an integer and p is a prime number such that p divides a and p divides (a+3). What can we deduce about p? why?

Since p divides a, a=np, for some integer n.
Since p divides a+3, a+3=mp, for some integer m.

Since a+3=mp and a=np then

np + 3 = mp (just substitute a=np above)

3 = mp - np

3 = p ( m - n )

So, p divides 3.

The only factors of 3 are 1 and 3.

Since p is prime, p must equal 3 since 1 is not a prime.

You don't have a statement. You have a question.

So a/p is an integer and (a+3)/p is also an integer.

(a+3)/p = a/p + 3/p

So 3/p must also be an integer

that requires that p = 1 or p=3