On Lucas Sequences Computation
نویسندگان
چکیده
منابع مشابه
On Lucas Sequences Computation
This paper introduces an improvement to a currently published algorithm to compute both Lucas “sister” sequences Vk and Uk. The proposed algorithm uses Lucas sequence properties to improve the running time by about 20% over the algorithm published in [1].
متن کاملOn generalized Lucas sequences
We introduce the notions of unsigned and signed generalized Lucas sequences and prove certain polynomial recurrence relations on their characteristic polynomials. We also characterize when these characteristic polynomials are irreducible polynomials over a finite field. Moreover, we obtain the explicit expressions of the remainders of Dickson polynomials of the first kind divided by the charact...
متن کاملOn squares in Lucas sequences
Let P and Q be non-zero integers. The Lucas sequence {Un(P,Q)} is defined by U0 = 0, U1 = 1, Un = PUn−1 − QUn−2 (n ≥ 2). The question of when Un(P,Q) can be a perfect square has generated interest in the literature. We show that for n = 2, ..., 7, Un is a square for infinitely many pairs (P,Q) with gcd(P,Q) = 1; further, for n = 8, ..., 12, the only non-degenerate sequences where gcd(P,Q) = 1 a...
متن کاملOn Perfect Powers in Lucas Sequences
Let (un)n≥0 be the binary recurrent sequence of integers given by u0 = 0, u1 = 1 and un+2 = 2(un+1 + un). We show that the only positive perfect powers in this sequence are u1 = 1 and u4 = 16. We also discuss the problem of determining perfect powers in Lucas sequences in general.
متن کاملOn a divisibility relation for Lucas sequences
Article history: Received 9 October 2015 Received in revised form 24 November 2015 Accepted 26 November 2015 Available online 8 January 2016 Communicated by Steven J. Miller MSC: 11B39
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ژورنال
عنوان ژورنال: Int'l J. of Communications, Network and System Sciences
سال: 2010
ISSN: 1913-3715,1913-3723
DOI: 10.4236/ijcns.2010.312128