Corpus ID: 224916368

Fermat's Last Theorem guarantees primes

@article{Elsholtz2020FermatsLT,
  title={Fermat's Last Theorem guarantees primes},
  author={C. Elsholtz},
  journal={arXiv: Number Theory},
  year={2020}
}
  • C. Elsholtz
  • Published 2020
  • Mathematics
  • arXiv: Number Theory
We show that Fermat's last theorem and a combinatorial theorem of Schur on monochromatic solutions of $a+b=c$ implies that there exist infinitely many primes. In particular, for small exponents such as $n=3$ or $4$ this gives a new proof of Euclid's theorem, as in this case Fermat's last theorem has a proof that does not use the infinitude of primes. Similarly, we discuss implications of Roth's theorem on arithmetic progressions, Hindman's theorem, and infinite Ramsey theory towards Euclid's… Expand

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