Arithmetic structure of recurrence sequences

2003 ◽  
pp. 93-115 ◽  
Author(s):  
Graham Everest ◽  
Alf van der Poorten ◽  
Igor Shparlinski ◽  
Thomas Ward
Keyword(s):  
Recurrence Sequences

scholarly journals Sums of Factorials in Binary Recurrence Sequences

2002 ◽  
Vol 93 (2) ◽  
pp. 87-107 ◽  
Author(s):  
George Grossman ◽  
Florian Luca
Keyword(s):  
Recurrence Sequences

scholarly journals A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences

2019 ◽  
Vol 194 ◽  
pp. 8-29 ◽  
Author(s):  
M. Ram Murty ◽  
François Séguin ◽  
Cameron L. Stewart
Keyword(s):  
Lower Bound ◽  
Prime Divisors ◽  
Recurrence Sequences

scholarly journals Positivity of Three-Term Recurrence Sequences

10.37236/329 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Lily L. Liu
Keyword(s):  
Sufficient Conditions ◽  
Recurrence Sequences

In this paper, we give the sufficient conditions for the positivity of recurrence sequences defined by $$a_nu_{n}=b_nu_{n-1}-c_nu_{n-2}$$ for $n\geqslant 2$, where $a_n,b_n,c_n$ are all nonnegative and linear in $n$. As applications, we show the positivity of many famous combinatorial sequences.

Divisor Sums of Generalised Exponential Polynomials

1996 ◽  
Vol 39 (1) ◽  
pp. 35-46 ◽  
Author(s):  
G. R. Everest ◽  
I. E. Shparlinski
Keyword(s):  
Prime Ideal ◽  
Algebraic Integer ◽  
Linear Recurrence ◽  
Exponential Polynomial ◽  
Exponential Polynomials ◽  
Recurrence Sequence ◽  
Special Cases ◽  
Divisor Sums ◽  
Recurrence Sequences

AbstractA study is made of sums of reciprocal norms of integral and prime ideal divisors of algebraic integer values of a generalised exponential polynomial. This includes the important special cases of linear recurrence sequences and general sums of S-units. In the case of an integral binary recurrence sequence, similar (but stronger) results were obtained by P. Erdős, P. Kiss and C. Pomerance.

scholarly journals Decomposable polynomials in second order linear recurrence sequences

2018 ◽  
Vol 159 (3-4) ◽  
pp. 321-346 ◽  
Author(s):  
Clemens Fuchs ◽  
Christina Karolus ◽  
Dijana Kreso
Keyword(s):  
Second Order ◽  
Linear Recurrence ◽  
Order Linear ◽  
Recurrence Sequences
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