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Explicit abc-conjecture and its applications

Abstract : 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.
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Submitted on : Saturday, January 19, 2019 - 9:23:00 AM
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Kwok Chi Chim, Saranya G. Nair, T. N. Shorey. Explicit abc-conjecture and its applications. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2019, Atelier Digit_Hum, pp.143 - 156. ⟨10.46298/hrj.2019.5117⟩. ⟨hal-01986721⟩

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