HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

# 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.
Keywords :
Document type :
Journal articles
Domain :

Cited literature [32 references]

https://hal.archives-ouvertes.fr/hal-01986721
Contributor : Srinivas Kotyada Connect in order to contact the contributor
Submitted on : Saturday, January 19, 2019 - 9:23:00 AM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM

### File

41Article17.pdf
Files produced by the author(s)

### Citation

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⟩

Record views