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

hrj:5117 - Hardy-Ramanujan Journal, January 23, 2019
Explicit abc-conjecture and its applications

Authors: Kwok , Chi Chim and Nair , Saranya G. and Shorey , T. N.

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.

Source : oai:HAL:hal-01986721v1
Published on: January 23, 2019
Submitted 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]