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An upper bound for the G.C.D. of two linear recurring sequences

In: Mathematica Slovaca, vol. 53, no. 1
Clemens Fuchs
Detaily:
Rok, strany: 2003, 21 - 42
O článku:
Let $(Gn)$ and $(Hn)$ be linear recurring sequences of integers defined by $Gn=c1α1n+c2α2n+…+ctαtn$ and $Hn=d1β1n+d2β2n+…+dsβsn$, where $t,s≥ 2$, $ci$, $dj$ are non-zero complex numbers and where $Gn$ does not divide $Hn$ in the ring of power sums. Then, provided $n>C1$, we have

$$ G.C.D.(Gn,Hn)<\vert Gn\vertc , $$

for all $n$ aside of a finite set of exceptions, whose cardinality can be bounded by $C2$, where $C1, C2$ and $c<1$ are effectively computable numbers depending on the $ci$, $dj$, $αi$ and $βj$, $i=1,…,t$, $j=1,…,s$. This quantifies a very recent result [Bugeaud, Y.—Corvaja, P.—Zannier, U.: {\it An upper bound for the $G.C.D.$ of $an-1$ and $bn-1$}, Math. Z. (To appear.)]
Ako citovať:
ISO 690:
Fuchs, C. 2003. An upper bound for the G.C.D. of two linear recurring sequences. In Mathematica Slovaca, vol. 53, no.1, pp. 21-42. 0139-9918.

APA:
Fuchs, C. (2003). An upper bound for the G.C.D. of two linear recurring sequences. Mathematica Slovaca, 53(1), 21-42. 0139-9918.