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Square classes of $(a\sp n-1)/(a-1)$ and $a\sp n+1$. (English) Zbl 0709.11014
J. Sichuan Univ., Nat. Sci. Ed. 26, Spec. Issue, 196-200 (1989).
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 $a,m,n<C$.
Reviewer: I.Gaál

11D41Higher degree diophantine equations