Things have been a little quiet lately on this blog; I was away for a bit on vacation, and I’m still catching up on some things, and I know Vishal has been busy. Hopefully we’ll have more posts soon.

In any case, it’s high time for another Problem of the Week! This one is undoubtedly classical in nature, but may require a famously nontrivial result to solve quickly by hand:

Find the length of the period of the repeating decimal representation of $\displaystyle \frac1{65537}.$

Please submit solutions to topological[dot]musings[At]gmail[dot]com by Friday, August 29, 11:59 pm (UTC); do not submit solutions in Comments. Everyone with a correct solution will be inducted into our Hall of Fame! We look forward to your response.