This is partly an explanation of my previous post.
I came up with a unique approach to the FLT equation over a year ago. I went looking for mathematicians and after difficulties, I managed to talk to a few. They were understandably skeptical and ultimately weren't interested. I managed to contact the AMS, partly at the suggestion of one of the mathematicians, and sent them what I had.
The original material had a claim that it was a proof, which was wrong, and this was explained to me by an editor at AMS. But, I was certain that there was something to what I had, and was heartened when I was told that the editor had never seen anything like it.
That could mean just about anything, so I finally started posting here. I didn't make any bold claims at first, but simply asked for help. I went over my method and gave it out as a curiosity, and requested information about its newness.
I found that no one had seen anything like it. However, I did get a couple of extremely negative responses which put me over the edge. Running into a wall, and not having an idea of what direction to go in, I started chasing phantom proofs and posting them, only to posts retractions and apologies later.
I finally cooled down and tried to let it all go, but I still felt there was reason for continued investigation. Finally, I worked out what I put in my post previous to this one and it appears to be finally solid.
The part for n=3 is easy but I still have trouble with the Q. I wanted something more easily worked out. If there is an error there, I want to know.
Lastly, I think part of the reason the folks at the AMS were so nice is that they recognized the possibilities in something that no one had seen before, but of course, given the history of the problem they didn't seriously believe that there was anything warranting interest. The rest of their niceness was just politeness and common decency, which is never wasted.