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Remark on factorials that are products of factorials.
- Source :
-
Mathematical Notes . Oct2010, Vol. 88 Issue 3/4, p317-320. 4p. - Publication Year :
- 2010
-
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)/ log 2) log log n and generalize it to the equation a! a! ... a! = n!. In a recent paper, F. Luca proved that n − b = 1 for large enough n provided that the ABC-hypothesis holds. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00014346
- Volume :
- 88
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Mathematical Notes
- Publication Type :
- Academic Journal
- Accession number :
- 55052326
- Full Text :
- https://doi.org/10.1134/S0001434610090038