Glasnik Matematicki, Vol. 47, No. 2 (2012), 285-293.

ON THE NUMBER OF DIVISORS OF n! AND OF THE FIBONACCI NUMBERS

Florian Luca and Paul Thomas Young

Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México
and
The John Knopfmacher Centre, for Applicable Analysis and Number Theory, University of the Witwatersrand, P.O. Wits 2050, South Africa
e-mail: fluca@matmor.unam.mx

Department of Mathematics, College of Charleston, Charleston, SC 29424, USA
e-mail: paul@math.cofc.edu


Abstract.   Let d(m) be the number of divisors of the positive integer m. Here, we show that if n {3,5}, then d(n!) is a divisor of n!. We also show that the only positive integers n such that d(Fn) divides Fn, where Fn is the nth Fibonacci number, are n {1,2,3,6,24,48}.

2010 Mathematics Subject Classification.   11N37, 11B39.

Key words and phrases.   Divisors, factorials, Fibonacci numbers.


Full text (PDF) (free access)

DOI: 10.3336/gm.47.2.05


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