[DC-3]

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?

[pathsjs]

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

[quickthrower2]

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!

[pathsjs]

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