Oh wow! I wouldn't have expected this so many years later. Mordel's conjecture implies asva special case that for all n>=4 there are only a finite number of solutions to Fermat's equations with relative prime numbers.
Brings me back!
> Mordel's conjecture implies as a special case that for all n>=4 there are only a finite number of solutions to Fermat's equations with relative prime numbers
I just learnt that fact from Wikipedia's article on Mordel's conjecture (now Faltings' theorem), was curious whether the theorem could be strengthened to obtain a full proof of Fermat’s Last Theorem (FLT) that is genuinely different from the Taylor–Wiles proof (or its later variants) and so asked an AI (in this case Grok via Twitter).
Grok correctly told me "no it's not possible", but then surfaced (as an aside) a nice expository article on the Taylor–Wiles proof by Faltings from AMS notices in July 1995, which I thought I'd share here:
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> Mordel's conjecture implies as a special case that for all n>=4 there are only a finite number of solutions to Fermat's equations with relative prime numbers
I just learnt that fact from Wikipedia's article on Mordel's conjecture (now Faltings' theorem), was curious whether the theorem could be strengthened to obtain a full proof of Fermat’s Last Theorem (FLT) that is genuinely different from the Taylor–Wiles proof (or its later variants) and so asked an AI (in this case Grok via Twitter).
Grok correctly told me "no it's not possible", but then surfaced (as an aside) a nice expository article on the Taylor–Wiles proof by Faltings from AMS notices in July 1995, which I thought I'd share here:
https://www.ams.org/notices/199507/faltings.pdf
The line is a breadthless legth.
Mordell conjecture is that only circles or figure contain infinite points, whereas curves with exponents over 3 are finite accumulations.