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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2010_88_3_a2,
     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/}
}
TY  - JOUR
AU  - K. G. Bhat
AU  - K. Ramachandra
TI  - Remark on Factorials that are Products of Factorials
JO  - Matematičeskie zametki
PY  - 2010
SP  - 350
EP  - 354
VL  - 88
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a2/
LA  - ru
ID  - MZM_2010_88_3_a2
ER  - 
%0 Journal Article
%A K. G. Bhat
%A K. Ramachandra
%T Remark on Factorials that are Products of Factorials
%J Matematičeskie zametki
%D 2010
%P 350-354
%V 88
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a2/
%G ru
%F MZM_2010_88_3_a2
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/

[1] F. Luca, “On factorials which are products of factorials”, Math. Proc. Cambridge Philos. Soc., 143:3 (2007), 533–542 | DOI | MR | Zbl

[2] R. C. Baker, G. Harman, J. Pintz, “The difference between consecutive primes. II”, Proc. London Math. Soc. (3), 83:3 (2001), 532–562 | DOI | MR | Zbl