Products of factorials which are powers
A. Bérczes, A. Dujella, L. Hajdu, N. Saradha, R. Tijdeman
Acta Arithmetica 190 (2019), 339-350
MSC: 11D41, 11D85.
DOI: 10.4064/aa171008-16-10
Opublikowany online: 29 July 2019
Streszczenie
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.
Autorzy
- A. BérczesInstitute of Mathematics
University of Debrecen
P.O. Box 12
H-4010 Debrecen, Hungary
e-mail
- A. DujellaDepartment of Mathematics
Faculty of Science
University of Zagreb
Bijenička cesta 30
10000 Zagreb, Croatia
e-mail
- L. HajduInstitute of Mathematics
University of Debrecen
P.O. Box 12, Hungary
H-4010 Debrecen
e-mail
- N. SaradhaINSA Senior Scientist
DAE - Center for Excellence in Basic Sciences
Mumbai University
Mumbai, India
e-mail
- R. TijdemanMathematical Institute
Leiden University
Postbus 9512
2300 RA Leiden, The Netherlands
e-mail