The latter.

Yes.Say if I have and , I could say this is: where , is this right?

If you mean "b + d is the remainder when a + c is divided by m", then not necessarily because b + d does not have to be less than m. For example,But if I do it the "long way" to get these:

Here, the is the remainder, right?

5 = 1 * 3 + 2

4 = 1 * 3 + 1

Adding these equations, we get 9 = 2 * 3 + 3. Here, 3 is not the remainder when 9 is divided by 3.

is correct. It is a special case of when p = q = 1.From , I convert to:

Here, I don't see similar to ... Am I not using the theorems correctly?