Fixed points and upper bounds for the rank of appearance in Lucas sequences

0398454 - MÚ 2014 RIV US eng J - Článek v odborném periodiku
Somer, L. - Křížek, Michal
Fixed points and upper bounds for the rank of appearance in Lucas sequences.
Fibonacci Quarterly. Roč. 51, č. 4 (2013), s. 291-306. ISSN 0015-0517
Institucionální podpora: RVO:67985840
Klíčová slova: Lucas sequences * prime numbers
Kód oboru RIV: BA - Obecná matematika

Let U(P,Q) denote the Lucas sequence satisfying the recursion relation Un+2 = PUn+1 − QUn, where U0 = 0, U1 = 1, and P and Q are integers. Let z(n), called the rank of appearance of n in U(P,Q), denote the least positive integer m such that Um 0 (mod n). We find all fixed points n for the rank of appearance such that z(n) = n. We also show that z(n) 2n when z(n) exists. This paper improves results considered by Diego Marques regarding the Fibonacci sequence.
Trvalý link: http://hdl.handle.net/11104/0225939