Lajos Hajdu, Márton Szikszai, Volker Ziegler
Published 2017-03-20Version 1
In this paper, we consider arithmetic progressions contained in Lucas sequences of first and second kind. We prove that for almost all sequences, there are only finitely many and their number can be effectively bounded. We also show that there are only a few sequences which contain infinitely many and one can explicitly list both the sequences and the progressions in them. A more precise statement is given for sequences with dominant root.
Discrepancy of Sums of two Arithmetic Progressions
Additive Volume of Sets Contained in Few Arithmetic Progressions
On elementary estimates for sum of some functions in certain arithmetic progressions
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