What number pairs mod n fulfill the condition $b \equiv (a+b) \mod n, with 1 \leq a,b, < n$?

(Note, $a,b = 0 \forall n$ is trivial.)

For example:

$6 \times 9 = 54 \equiv 2 \mod 13$.

$6 + 9 = 15 \equiv 2 \mod 13$.

(Also, the familiar $2 \times 2 = (2+2) \mod 10$.

Related note:

From what I can see, modulo $n$ and base $n$ are related by the fact that the 0-th power term of $x$ base $n$ is equal to $x \mod n$.