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Roth's Theorem implies a Weakened Version of the ABC Conjecture for Special Cases

Philipp Sibbertsen, Karsten Müller, Timm Lampert and Michael Taktikos

Hannover Economic Papers (HEP) from Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät

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: Roth's Theorem; ABC Conjecture (search for similar items in EconPapers)
JEL-codes: C02 C60 (search for similar items in EconPapers)
Pages: 8 pages
Date: 2022-07
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