TY - JOUR
T1 - Sums of factorials in binary recurrence sequences
AU - Grossman, George
AU - Luca, Florian
N1 - Funding Information:
1Work by the second author was supported in part by the Alexander von Humboldt foundation and in part by the program KONTAKT ME 148 of the Czech Republic.
PY - 2002
Y1 - 2002
N2 - In this paper, we consider the problem of expressing a term of a given non-degenerate binary recurrence sequence as a sum of factorials. We show that if one bounds the number of factorials allowed, then there are only finitely many effectively computable terms which can be represented in this way. As an application, we also find the largest members of the classical Fibonacci and Lucas sequences which can be written as a sum or a difference of two factorials.
AB - In this paper, we consider the problem of expressing a term of a given non-degenerate binary recurrence sequence as a sum of factorials. We show that if one bounds the number of factorials allowed, then there are only finitely many effectively computable terms which can be represented in this way. As an application, we also find the largest members of the classical Fibonacci and Lucas sequences which can be written as a sum or a difference of two factorials.
UR - http://www.scopus.com/inward/record.url?scp=0036109553&partnerID=8YFLogxK
U2 - 10.1006/jnth.2001.2718
DO - 10.1006/jnth.2001.2718
M3 - Article
AN - SCOPUS:0036109553
SN - 0022-314X
VL - 93
SP - 87
EP - 107
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -