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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