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 = Fq[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 gi = 0 for the linear recurrent, Fibonacci-like, sequence defined by g0 = 0, g1 = 1 and Keywords: Polynomials; euclidean division; finite fields; even characteristic. AMS Subject classification: Primary: 11T55, 11T06, 11B39 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2011, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |