Article contents
The Number of Non-Zero Digits of n!
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Let $b$ be an integer with
$b\,>\,1$. In this note, we prove that the number of non-zero digits in the base
$b$ representation of
$n!$ grows at least as fast as a constant, depending on
$b$, times
$\log \,n$.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2002
References
[1]
Bugeaud, Y. and Laurent, M.,Minoration effective de la distance p-adique entre puissances de nombres algébriques. J. Number Theory (2) 61 (1996), 311–342.Google Scholar
[2]
Erdoʺs, P. and Oblath, R., Ü ber diophantishe Gleichungen der Form n! = xp ± yp und n! ± m! = xp
. Acta Litt. Sci. Szeged 8 (1937), 241–255.Google Scholar
[4]
Luca, F., Distinct digits in base b expansions of linear recurrence sequences. Quaestiones Math., to appear.Google Scholar
[5]
Stewart, C. L., On the representation of an integer in two different bases. J. Reine Angew. Math. 319 (1980), 63–72.Google Scholar
- 7
- Cited by