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.
But you're judging the writers for not knowing something would happen. From their point of view the Theorem hadn't been solved in 300 years so they certainly didn't expect it to get solved inside the next 300 years let alone the next few. The thing is that knowing what we know NOW we have to rationalize the error so that it makes sense.
It's like how in "The Voyage Home" there's some lip service to Leningrad. Oops! They forgot to predict the fall of the Soviet Union and Leningrad reverting to Sait Petersberg. Are we going to blame the writers of TVH for failing to predict the fall of the Soviet Union and for the renaming of the city?