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 -