Double exponential lower bounds for possible solutions in the Second Case of the Fermat Last Theorem
Number Theory
2021-08-20 v1
Abstract
In a recent paper, the first author provided some lower bounds to solutions of the equations of Fermat and Catalan, based on local power series developments at the ramified prime of a prime cyclotomic extension. Although both equations have in fact been proved not to have any unknown solutions, these improved bounds are interesting in the context of a new effective abc inequality announced in the paper \cite{MFHMP} based on Mochizuki's \cite{Mo}[IUT-IV, Theorem A]. In this paper we provide a strengthening of the lower bound for FLT2, which is necessary in order to take advantage of the best upper bounds for primes for which it was verified on a computer that FLT2 has no solutions.
Keywords
Cite
@article{arxiv.2108.08580,
title = {Double exponential lower bounds for possible solutions in the Second Case of the Fermat Last Theorem},
author = {Preda Mihăilescu and Michael T. Rassias},
journal= {arXiv preprint arXiv:2108.08580},
year = {2021}
}
Comments
Submitted, under review