eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2019-01-23
10.46298/hrj.2019.5117
5117
journal article
Explicit abc-conjecture and its applications
Chi Chim Kwok
Saranya G. Nair
T. N. Shorey
We state well-known abc-conjecture of Masser-OesterlĂ© 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.
https://hrj.episciences.org/5117/pdf
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]