On Some Combinations of Non-Consecutive Terms of a Recurrence Sequence
Department of Mathematics
Faculty of Science
University of Hradec Králové
Let (Gm)m≥0 be an integer
linear recurrence sequence (satisfying some weak technical conditions)
and let x ≥ 1 be an integer. In this paper, among other things,
we are interested in non-consecutive combinations
Gn that belong to the sequence
(Gm)m≥0 for infinitely many
positive integers n. In this case, we make explicit an upper
bound for x that depends only on a and the zeros of the
characteristic polynomial of this recurrence (this generalizes previous
papers of Trojovský). As an application, we study the Fibonacci case.
Full version: pdf,
(Concerned with sequence
Received February 19 2018; revised version received March 11 2018.
Published in Journal of Integer Sequences, March 12 2018.
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