Hardy Ramanujan Journal |

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,
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MATH
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Mathematics [math],
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MATH.MATH-NT
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Mathematics [math]/Number Theory [math.NT]