{"docId":5117,"paperId":5117,"url":"https:\/\/hrj.episciences.org\/5117","doi":"10.46298\/hrj.2019.5117","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01986721","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-01986721v1","dateSubmitted":"2019-01-23 14:22:25","dateAccepted":"2019-01-23 15:40:44","datePublished":"2019-01-23 15:40:55","titles":{"en":"Explicit abc-conjecture and its applications"},"authors":["Kwok , Chi Chim","Nair , Saranya G.","Shorey , T. N."],"abstracts":{"en":"We state well-known abc-conjecture of Masser-Oesterl\u00e9 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."},"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]"]}