Chi Chim Kwok ; Saranya G. Nair ; T. N. Shorey - Explicit abc-conjecture and its applications

hrj:5117 - Hardy-Ramanujan Journal, January 23, 2019 - https://doi.org/10.46298/hrj.2019.5117
Explicit abc-conjecture and its applicationsArticle

Authors: Chi Chim Kwok ; Saranya G. Nair 1; T. N. Shorey 2

  • 1 Indian Statistical Institute [Bangalore]
  • 2 National Institute of Advanced Studies

We state well-known abc-conjecture of Masser-Oesterlé and its explicit version, popularly known as the explicit abc-conjecture, due to Baker. Laishram and Shorey derived from the explicit abc-conjecture that (1.1) implies that $c < N^{1.75}$. We give a survey on improvements of this result and its consequences. Finally we prove that $c < N^{1.7}$ and apply this estimate on an equation related to a conjecture of Hickerson that a factorial is not a product of factorials non-trivially.


Published on: January 23, 2019
Imported on: January 23, 2019
Keywords: Primes,factorials,abc-conjecture,explicit conjecture,Diophantine equations 2010 Mathematics Subject Classification 11A41,11B25,11N13,11D41,11Z05, [ MATH ] Mathematics [math], [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]
Funding:
    Source : OpenAIRE Graph
  • Diophantine Problems: Analytic, geometric and computational aspects; Funder: Austrian Science Fund (FWF); Code: P 26114

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