Find minimum integer $n$ and $m$ such that $36^n = 16^m, n \in \mathbb{Z}, m \in \mathbb{Z}$?

Question

How would I go about finding the minimum $n$ and $m$ such that $36^n = 16^m, n \in \mathbb{Z}, m \in \mathbb{Z}$?

The practical reason for this is that I would like to find the minimum number of hex characters such that I can evenly convert it to base 36.

Answer 1

If $n,m \, \geq 1$ then $3 | 36^n = 2^{4m}$.

Answer 2

This is equivalent to finding integer solutions for $3^{2n}=2^{4m-2n}$

Obviously, the only integer solutions would be $n=m=0$