✦ LIBER ✦

The Square Terms in Lucas Sequences

✍ Scribed by Paulo Ribenboim; Wayne L. McDaniel

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 579 KB
Volume: 58
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0068

No coin nor oath required. For personal study only.

✦ Synopsis

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 a square. The condition D>0 assures that the result holds for all such sequences whose terms are positive.

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