Remark on factorials that are products of factorials

Bhat, Kishor G and Ramachandra, K (2010) Remark on factorials that are products of factorials. Math Notes, 88. pp. 317-320.

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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 1!a 2! ... a k ! = 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
Keywords: factorial product of factorials, Stirling’s formula, prime factor
Subjects: School of Natural and Engineering Sciences > Mathematics
Doctoral Programme > PhD Scholar Publications
Date Deposited: 22 Apr 2021 17:27
Last Modified: 29 Apr 2021 16:51
Official URL: https://link.springer.com/article/10.1134/S0001434...
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    Funders: UNSPECIFIED
    Projects: UNSPECIFIED
    DOI: https://doi.org/10.1134/S0001434610090038
    URI: http://eprints.nias.res.in/id/eprint/2087

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