Explicit abc-conjecture and its applications
Kwok Chi , Chim ; Nair, Saranya G. ; Shorey, T. N.
HAL, hal-01986721 / Harvested from HAL
Text on HAL
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.
Publié le : 2019-01-23
Classification:  11B25,  Diophantine equations 2010 Mathematics Subject Classification 11A41,  11Z05,  11D41,  11N13,  Primes,  factorials,  abc-conjecture,  explicit conjecture,  [MATH]Mathematics [math],  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] 
@article{hal-01986721,
     author = { Kwok Chi , Chim and Nair, Saranya G. and Shorey, T. N.},
     title = {Explicit abc-conjecture and its applications},
     journal = {HAL},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01986721}
}

 Kwok Chi , Chim; Nair, Saranya G.; Shorey, T. N. Explicit abc-conjecture and its applications. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-01986721/