Geodesic
Products of factorials which are powers
A. Bérczes 1   ; A. Dujella 2   ; L. Hajdu 3   ; N. Saradha 4   ; R. Tijdeman 5
1 Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary
2 Department of Mathematics Faculty of Science University of Zagreb Bijenička cesta 30 10000 Zagreb, Croatia
3 Institute of Mathematics University of Debrecen P.O. Box 12, Hungary H-4010 Debrecen
4 INSA Senior Scientist DAE - Center for Excellence in Basic Sciences Mumbai University Mumbai, India
5 Mathematical Institute Leiden University Postbus 9512 2300 RA Leiden, The Netherlands
Acta Arithmetica, Tome 190 (2019) no. 4, pp. 339-350 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Extending earlier research of Erdős and Graham, we consider the problem of products of factorials yielding perfect powers. On the one hand, we describe how the representability of $\ell$th powers behaves when the number of factorials is smaller than, equal to or larger than $\ell$, respectively. On the other hand, we investigate for which fixed $n=b_1$ it is possible to find integers $b_2,\dots,b_k$ at most $b_1$ (obeying certain conditions) such that $b_1!\cdots b_k!$ is a perfect power. Here we distinguish the cases where the factorials may be repeated or are distinct.
DOI : 10.4064/aa171008-16-10
Keywords: extending earlier research erd graham consider problem products factorials yielding perfect powers describe representability ellth powers behaves number factorials smaller equal larger ell respectively other investigate which fixed possible integers dots obeying certain conditions cdots perfect power here distinguish cases where factorials may repeated distinct

A. Bérczes  1   ; A. Dujella  2   ; L. Hajdu  3   ; N. Saradha  4   ; R. Tijdeman  5

1 Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary
2 Department of Mathematics Faculty of Science University of Zagreb Bijenička cesta 30 10000 Zagreb, Croatia
3 Institute of Mathematics University of Debrecen P.O. Box 12, Hungary H-4010 Debrecen
4 INSA Senior Scientist DAE - Center for Excellence in Basic Sciences Mumbai University Mumbai, India
5 Mathematical Institute Leiden University Postbus 9512 2300 RA Leiden, The Netherlands 
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     author = {A. B\'erczes and A. Dujella and L. Hajdu and N. Saradha and R. Tijdeman},
     title = {Products of factorials which are powers},
     journal = {Acta Arithmetica},
     pages = {339--350},
     year = {2019},
     volume = {190},
     number = {4},
     doi = {10.4064/aa171008-16-10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa171008-16-10/}
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A. Bérczes; A. Dujella; L. Hajdu; N. Saradha; R. Tijdeman. Products of factorials which are powers. Acta Arithmetica, Tome 190 (2019) no. 4, pp. 339-350. doi: 10.4064/aa171008-16-10

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