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

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

If $x$ denote the number of elements in $S$ then what is the value of $x$?

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