Geodesic
Remark on Factorials that are Products of Factorials
Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 350-354

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In a paper published in 1993, Erdős proved that if $n!=a!b!$, where $1$, 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 $((1+\epsilon)/\log 2)\log\log n$ and generalize it to the equation $a_1!a_2!\dots a_k!=n!$. In a recent paper, F. Luca proved that $n-b=1$ for large enough $n$ provided that the ABC-hypothesis holds.
Keywords: factorial, product of factorials, Stirling's formula, prime factor. 
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     author = {K. G. Bhat and K. Ramachandra},
     title = {Remark on {Factorials} that are {Products} of {Factorials}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {350--354},
     publisher = {mathdoc},
     volume = {88},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a2/}
}
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K. G. Bhat; K. Ramachandra. Remark on Factorials that are Products of Factorials. Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 350-354. http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a2/