10.46298/hrj.2019.5117
https://hrj.episciences.org/5117
Kwok
,
Chi Chim
Chi Chim
Kwok
Nair
,
Saranya G.
Saranya G.
Nair
Shorey
,
T. N.
T. N.
Shorey
Explicit abc-conjecture and its applications
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.
episciences.org
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]
2019-01-23
2019-01-23
2019-01-23
en
journal article
https://hal.archives-ouvertes.fr/hal-01986721v1
2804-7370
https://hrj.episciences.org/5117/pdf
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