Lower bounds for the greatest prime factor of product of consecutive positive integers

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• 作者：Saranya G. Nair ; ^{saranya@math.iitb.ac.in" class="auth_mail" title="E-mail the corresponding author} ; T.N. Shorey ^{shorey@math.iitb.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11A41 ; 11D45 ; 11D72
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：159
• 期：Complete
• 页码：307-328
• 全文大小：417 K

文摘

Under Baker's explicit abc conjecture, we completely solve a conjecture of Hickerson when a product of two or more factorials is equal to n! for a given positive integer n  . We also prove it unconditionally when n id="mmlsi1" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15002474&_mathId=si1.gif&_user=111111111&_pii=S0022314X15002474&_rdoc=1&_issn=0022314X&md5=6923a9788add3ac959b75f7bb80d0722" title="Click to view the MathML source">n≤e⁸⁰n>n class="mathContainer hidden">n class="mathCode">th altimg="si1.gif" overflow="scroll">n≤en>80n>th>n>n>n>. The proofs depend on sharpening the lower bounds on the greatest prime factor of a product of consecutive positive integers.