Prove that there exists an infinite number of values $n \in \mathbb{N}^*$ such that $3n+1 \mid 2^n-1$.
I tried constructing a number with such property using $n,m$ such that $3n+1 \mid 2^n-1$ and $3m+1 \mid 2^m-1$. I also thought about using polynomials, but I failed.
Examples of $n$ that works: $10, 14, 36, 42, 52$.