p. 213 - 220 On explicit formulae and linear recurrent sequences
R. Euler and L. H. Gallardo Received: June 6, 2010;
Accepted: March 17, 2011
Abstract.
We notice that some recent explicit results about linear recurrent
sequences over a ring $R$ with 1 were already obtained by Agou in
a 1971 paper by considering the euclidean division of polynomials
over R. In this paper we study an application of these results to
the case when R =
F_{q}[t] and q is even, completing Agou's work.
Moreover, for even q we prove that there is an infinity of
indices i such that g = 0 for the linear recurrent, Fibonacci-like,
sequence defined by _{i}g_{0} = 0, g_{1} = 1 and g_{n + 1} =
g + D
_{n}g_{n - 1}
n > 1, where D is any
nonzero polynomial in R =
F_{q}[t]
A new identity is established.
Keywords:
Polynomials; euclidean division; finite fields; even characteristic.
AMS Subject classification:
Primary: 11T55, 11T06, 11B39
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