I don't mean to be terse or impolite, but that was one reason I used the word "attempted" in my previous post. It well may be that, a) the approach I attempted is not suitable to the task; and/or b) I have not implemented the approach properly.
However, with that being said, I think the fact...
Since I'm not sure at this point if the approach I had attempted will be successful, I'll just say what I had intended that approach to be. The thing that makes the n=2 version of the functions in the generalized version of the Pythagorean theorem unique, is the fact that the second derivative...
I had thought that it would be unnecessary, but Dodo had already convinced me of my error. I will be working on this and will post when I either have something useful to add or it becomes obvious to me that I was premature.
I'm not a mathematician so I probably won't understand your question, but I'll give it my best shot.
The remaining series together with the value of n would have to resolve to a value of either 0 for when n is an odd number and -2 when n is an even number.
When n is odd and equal to 3 or...
I'm sure there are mistakes here so criticism is welcome. In the unlikely event someone would like to sponsor my article for ArXiv, please let me know.
http://www.non-ducor.com/fj/Algebraic_proof_of_Fermats_conjecture_001.png...