Comment by prerok
Well, true, we cannot be 100% certain, but if he published the proof to n=4, we can say it's most likely he did not find the general proof.
Well, true, we cannot be 100% certain, but if he published the proof to n=4, we can say it's most likely he did not find the general proof.
Because if he had the general proof he wouldn't need to go out of his way to prove n=4, since it would be covered already by the general proof
It is simply an obvious fault line in the nature of the problem statement: you can crack the problem in 2 parts: the x^4+y^4=z^4 part, and the part that claims x^p+y^p=z^p with p a prime.
Suppose Fermat solved the proof by using this natural fault line -its just how this cookie crumbles- solved the n=4 case, and then smashed his head a thousand times against the problem and finally found the prime n proof.
He challenges the community, and since they don't take up the challenge, "encourages" them in a manner that may be described as trollish, by showing how to do the n=4 case. (knowing full well the prime power case proof looks totally different)
That's an interesting take but I think it's unlikely for two reasons:
1. In any case you view it, it's not trivial, which was the statement in the note. If it were, the effort to publish just for n=4 would be silly, because it would take equal effort to just publish for general case. That he withheld the proof just to mess with people is highly unlikely.
2. I definitely do not make private notes in my books just so that maybe somebody later on would pick up that book and wonder whether I had indeed discovered the secrets of the universe. I definitely do not write "challenges to the community" there.
why does that make it more likely?