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arXiv · 2108.08580

Double exponential lower bounds for possible solutions in the Second Case of the Fermat Last Theorem

Preda Mihăilescu·Michael T. Rassias
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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 $p$ for which it was verified on a computer that FLT2 has no solutions.

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BibTeXRIS

Preda Mihăilescu, Michael T. Rassias. 2021-08-19. Double exponential lower bounds for possible solutions in the Second Case of the Fermat Last Theorem. https://arxiv.org/abs/2108.08580

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