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Zbl 0709.11014
Ribenboim, Paulo
Square classes of $(a\sp n-1)/(a-1)$ and $a\sp n+1$. (English)
[J] J. Sichuan Univ., Nat. Sci. Ed. 26, Spec. Issue, 196-200 (1989). ISSN 0490-6756

Let $a>1$, $n\ge 1$ be integers, $U\sb n=(a\sp n-1)/(a-1)$, $V\sb n=a\sp n+1$. The author studies the square classes of the second order linear recurrence sequences $U\sb n,V\sb n$, that is the question when $U\sb mU\sb n$ or $V\sb mV\sb nis$ a square with distinct m,n. It is proved that $U\sb mU\sb n$ can not be a square with $m\ne n$. The same is shown for the sequence $V\sb n$ if a is even. If a is odd, then there exist an effectively computable constant C such that if $V\sb mV\sb n$ is square with $m\ne n$ then $a,m,n<C$.
[I.Gaál]

MSC 2000:: *11B37 Recurrences
11D41 Higher degree diophantine equations

Keywords: square classes; second order linear recurrence sequences

Cited in: Zbl 0923.11036

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