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Comment by quickthrower2 | Hacker News Reader

I still want to know what was the proof Fermat wrote was that couldn't fit in a margin.

Despite Fermat's brilliance, it's barely feasible that such a proof exists after 300 years of attempts by professionals and amateurs alike.

Ironically though, the tantalising idea of the existence of a simple proof - motivated by that infamous quote - contributed massively (along with the simplicity of the conjecture itself) to the theorem's notoriety and the myriad attempts to solve it.

Fermat was a brilliant social engineer as well as mathematician.

It's the predecessor of the dictum about putting a wrong answer on the internet to get the right answer. Sorta, and with a few hundred years involved.

He wrote the note to himself, a long time before he died. He then publicly announced a proof for the n=4 case, and nothing about the general case. It strongly suggests that he realized his proof was wrong.

It seems there's a fair chance it was a flawed proof, in which case I doubt we'll ever be particularly confident although we could possibly surface some candidates.

Something I always wondered is if we know of the existence of a proof that is both simple and also non-obviously flawed and as such could have been Fermat's solution?

Yes, Lamé solution, which assumes unique factorization in the rings of integers of cyclotomic fields, and can in fact be salvaged to prove the case of regular primes

Thanks while I don't fully understand what this means I think I get the idea. I assume it's a proof that has the "n" over infinite many cases (primes) but not all of them? Googling it was hard because there are other Lamé things. I'll just imagine he wrote this proof. Not the full proof, but not lame!

Yes, for some details look at http://fermatslasttheorem.blogspot.com/2006/01/lams-proposed... or https://math.stackexchange.com/questions/953462/what-was-lam...

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