Remark on factorials that are products of factorials

Bhat, K. G. ; Ramachandra, K. (2010) Remark on factorials that are products of factorials Mathematical Notes, 88 (3-4). pp. 317-320. ISSN 0001-4346

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Official URL: http://www.springerlink.com/content/511hx5t27p1110...

Related URL: http://dx.doi.org/10.1134/S0001434610090038

Abstract

In a paper published in 1993, Erdös proved that if n!=a! b!, where 1 < a≤b, then the difference between n and b does not exceed 5 log log n for large enough n. In the present paper, we improve this upper bound to ((1+ε)/log2)log logn and generalize it to the equation a1!a2!... ak!=n!. In a recent paper, F. Luca proved that n−b=1 for large enough n provided that the ABC-hypothesis holds.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Factorial; Product of Factorials; Stirling's Formula; Prime Factor
ID Code:49194
Deposited On:19 Jul 2011 09:45
Last Modified:19 Jul 2011 09:45

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