I got this from the exercise in the introductory chapter of Velleman's "How to Prove It."

Exercise 1b: Find an integer $\displaystyle x$

$\displaystyle 1<x<2^{32767}-1$ and $\displaystyle 2^{32767}-1$ is divisible by $\displaystyle x$.

I have got $\displaystyle 32767 = 2^{(31)(1057)}$, such that $\displaystyle x= 2^{1057}-1$ and that

$\displaystyle \frac{2^{32767}-1}{2^{1057}-1}$

$\displaystyle log_{10} (y) = log_{10} (2^{32767}-1) - log_{10}(2^{1057}-1)$ is too large to handle.

$\displaystyle log_2 (y) = log_2 (2^{32767}-1) - log_2(2^{1057}-1)$ is unmanageable.

$\displaystyle log_2$ is a foreign language to me. I don't know how to proceed from here.

Someone please help.