Among the statements:\\
$(S1): 2023^{2022} - 1999^{2022}$ is divisible by 8.\\
$(S2): 13(13)^{n} - 11n - 13$ is divisible by 144 for infinitely many $n \in \mathbb{N}$\\
(1) Only $(S2)$ is correct\\
(2) Only $(S1)$ is correct\\
(3) Both $(S1)$ and $(S2)$ are correct\\
(4) Both $(S1)$ and $(S2)$ are incorrect