Are there infinitely many elements in this set

S={nN : 2n(3n1)}\large S =\bigl\{ n \in \mathbb{N} \ : \ 2^{n} \mid (3^{n}-1) \bigr\}

Let N \mathbb{N} denote the set of natural numbers and let S S denote the set above.

If xx denote the number of elements in SS then what is the value of xx ?

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