On squares in Lucas sequences
| dc.creator | Bremner, A. | |
| dc.creator | Tzanakis, N. | |
| dc.date | 2006-10-24 | |
| dc.date.accessioned | 2026-07-07T07:29:23Z | |
| dc.date.available | 2026-07-07T07:29:23Z | |
| dc.description | Let P and Q be non-zero integers. The Lucas sequence U_n(P,Q) is defined by U_0=0, U_1=1, U_n= P*U_{n-1}-Q*U_{n-2} for n >1. The question of when U_n(P,Q) can be a perfect square has generated interest in the literature. We show that for n=2,...,7, U_n 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 and U_n(P,Q)=square, are given by U_8(1,-4)=21^2, U_8(4,-17)=620^2, and U_12(1,-1)=12^2. | |
| dc.description | 11 pages. To appear in Journal of Number Theory | |
| dc.identifier | https://arxiv.org/abs/math/0610732 | |
| dc.identifier | http://arxiv.org/abs/math/0610732 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118088 | |
| dc.subject | Number Theory | |
| dc.subject | 11B37; 11D41; 11G05; 11G30 | |
| dc.title | On squares in Lucas sequences | |
| dc.type | text |