Results 1 
3 of
3
On the order of Stirling numbers and alternating binomial coefficient sums, The Fibonacci Quarterly
, 2001
"... We prove that the order of divisibility by prime p of k! S(a(p − 1) pq,k)doesnot depend on a and q if q is sufficiently large and k/p is not an odd integer. Here S(n, k) denotes the Stirling number of the second kind; i.e., the number of partitions of a set of n objects into k nonempty subsets. The ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
We prove that the order of divisibility by prime p of k! S(a(p − 1) pq,k)doesnot depend on a and q if q is sufficiently large and k/p is not an odd integer. Here S(n, k) denotes the Stirling number of the second kind; i.e., the number of partitions of a set of n objects into k nonempty subsets. The proof is based on divisibility results for psected alternating
The 2adic Order of the Tribonacci Numbers and the Equation T n = m!
, 2014
"... Abstract Let (T n ) n≥0 be the Tribonacci sequence defined by the recurrence T n+2 = T n+1 + T n + T n−1 , with T 0 = 0 and T 1 = T 2 = 1. In this paper, we characterize the 2adic valuation of T n and, as an application, we completely solve the Diophantine equation T n = m!. ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract Let (T n ) n≥0 be the Tribonacci sequence defined by the recurrence T n+2 = T n+1 + T n + T n−1 , with T 0 = 0 and T 1 = T 2 = 1. In this paper, we characterize the 2adic valuation of T n and, as an application, we completely solve the Diophantine equation T n = m!.
On Generalized Cullen and Woodall Numbers That are Also Fibonacci Numbers
, 2014
"... Abstract The mth Cullen number C m is a number of the form m2 m + 1 and the mth Woodall number W m has the form m2 m − 1. In 2003, Luca and Stȃnicȃ proved that the largest Fibonacci number in the Cullen sequence is F 4 = 3 and that F 1 = F 2 = 1 are the largest Fibonacci numbers in the Woodall se ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract The mth Cullen number C m is a number of the form m2 m + 1 and the mth Woodall number W m has the form m2 m − 1. In 2003, Luca and Stȃnicȃ proved that the largest Fibonacci number in the Cullen sequence is F 4 = 3 and that F 1 = F 2 = 1 are the largest Fibonacci numbers in the Woodall sequence. A generalization of these sequences is defined by C m,s = ms m + 1 and W m,s = ms m − 1, for s > 1. In this paper, we search for Fibonacci numbers belonging to these generalized Cullen and Woodall sequences.