Among the statements : (S1) : $2023^{2022}-1999^{2022}$ is divisible by 8 (S2) : $13(13)^{n}-12 n-13$ is divisible by 144 for infinitely many $n \in \mathbb{N}$

Question

Among the statements :

(S1) : $2023^{2022}-1999^{2022}$ is divisible by 8

(S2) : $13(13)^{n}-12 n-13$ is divisible by 144 for infinitely many $n \in \mathbb{N}$

both (S1) and (S2) are incorrect

only (S1) is correct

only (S2) is correct

both (S1) and (S2) are correct

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