Roth's Theorem implies a Weakened Version of the ABC Conjecture for Special Cases
Number Theory
2022-08-31 v1
Abstract
Enrico Bombieri proved that the ABC Conjecture implies Roth's theorem in 1994. This paper concerns the other direction. In making use of Bombieri's and Van der Poorten's explicit formula for the coefficients of the regular continued fractions of algebraic numbers, we prove that Roth's theorem implies a weakened non-effective version of the ABC Conjecture in certain cases relating to roots.
Keywords
Cite
@article{arxiv.2208.14354,
title = {Roth's Theorem implies a Weakened Version of the ABC Conjecture for Special Cases},
author = {Philipp Sibbertsen and Timm Lampert and Karsten Müller and Michael Taktikos},
journal= {arXiv preprint arXiv:2208.14354},
year = {2022}
}