On Pillai's problem with the Fibonacci and Pell sequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA200245J" target="_blank" >RIV/61988987:17310/19:A200245J - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs40590-018-0223-9" target="_blank" >https://link.springer.com/article/10.1007%2Fs40590-018-0223-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40590-018-0223-9" target="_blank" >10.1007/s40590-018-0223-9</a>

Result language
angličtina
Original language name
On Pillai's problem with the Fibonacci and Pell sequences
Original language description
Let (F-n)(n >= 0) and (P-n)(n >= 0) be the Fibonacci and Pell sequences given by the initial conditions F-0 = 0, F-1 = 1, P-0 = 0, P-1 = 1 and the recurrence formulas Fn+2 = Fn+1 + F-n, Pn+2 = 2P(n+1) + P-n for all n >= 0, respectively. In this note, we study the Pillai type problem: F-n - P-m = F-n1 - P-m1 in non-negative integer pairs (n, m) not equal (n(1), m(1)). We completely solve this equation.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

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