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

Author

Listed:
  • Sibbertsen, Philipp
  • Müller, Karsten
  • Lampert, Timm
  • Taktikos, Michael

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.

Suggested Citation

  • Sibbertsen, Philipp & Müller, Karsten & Lampert, Timm & Taktikos, Michael, 2022. "Roth's Theorem implies a Weakened Version of the ABC Conjecture for Special Cases," Hannover Economic Papers (HEP) dp-700, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    • Handle: RePEc:han:dpaper:dp-700
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    Keywords

    Roth's Theorem; ABC Conjecture;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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