Are there infinitely many positive integers $n$ such that $n$ divides $3^{6n-1} - 1$?
I guess the answer should be positive and the only reasonable idea I have is to consider $n = 3^k - 1$ since if $k$ divides $6 \cdot 3^k - 7$ we will be done - but I do not know if this can be used nicely.
Any help appreciated!