It's also likely the current solution is debated in the 24c or people are trying to find other solutions.
Well, I'm not ready to give a writer credit for something he didn't bother to include, especially for a script that's as poorly written as The Royal. The whole entire point of even using Fermat's Last Theorem was just a means of brushing off questions this episode may have raised.
Riker: Why did this happen?
Picard: We may never know, JUST LIKE FERMAT'S LAST THEOREM!
Now you may add that not having the answers to everything can make a story more interesting, and I would agree. But remember, this episode takes place on a planet where the temperature is somehow below absolute zero with an alien species that put a single human in a poorly thought out recreation and left him to die. The reason we don't get any answers to these questions is because the writer simply wrote a 'situation' story, not an actual story that carries any meaning. Oh, it certainly tried to with the Theorem bit, but unfortunately, that didn't last.