# Are there infinitely many elements in this set

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

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 $$x$$?

×