On the discriminator of Lucas sequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA20023P3" target="_blank" >RIV/61988987:17310/19:A20023P3 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs40316-017-0097-7" target="_blank" >https://link.springer.com/article/10.1007%2Fs40316-017-0097-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40316-017-0097-7" target="_blank" >10.1007/s40316-017-0097-7</a>

Result language
angličtina
Original language name
On the discriminator of Lucas sequences
Original language description
We consider the family of Lucas sequences uniquely determined by Un+2(k) = (4k + 2)Un+1(k) - U-n(k), with initial values U-0(k) = 0 and U-1(k) = 1 and k >= 1 an arbitrary integer. For any integer n >= 1 the discriminator function D-k(n) of U-n(k) is defined as the smallest integer m such that U-0(k), U-1(k), ... ,Un-1(k) are pairwise incongruent modulo m. Numerical work of Shallit on D-k(n) suggests that it has a relatively simple characterization. In this paper we will prove that this is indeed the case by showing that for every k >= 1 there is a constant n(k) such that D-k(n) has a simple characterization for every n >= nk. The case k = 1 turns out to be fundamentally different from the case k > 1.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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