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On squares in Lucas sequences

✍ Scribed by A. Bremner; N. Tzanakis

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
145 KB
Volume
124
Category
Article
ISSN
0022-314X

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πŸ“œ SIMILAR VOLUMES

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Let [U n (P, Q)] and [V n (P, Q)] denote the Lucas sequence and companion Lucas sequence, respectively, with parameters P and Q. For all odd relatively prime values of P and Q such that D=P 2 &4Q is positive, we determine all indices n such that U n (P, Q), 2U n (P, Q), V n (P, Q) or 2V n (P, Q) is

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Let P and Q be non-zero relatively prime integers. The Lucas sequence fU n Γ°P; QÞg is defined by We show that the only sequence with U 12 Γ°P; QÞ a perfect square is the Fibonacci sequence fU n Γ°1; Γ€1Þg; and we show that there are no non-degenerate sequences fU n Γ°P; QÞg with U 9 Γ°P; QÞ a perfect sq