Pillai's problem with the Fibonacci and Padovan sequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA2002489" target="_blank" >RIV/61988987:17310/19:A2002489 - isvavai.cz</a>
Result on the web
<a href="http://publikacio.uni-eszterhazy.hu/4502/" target="_blank" >http://publikacio.uni-eszterhazy.hu/4502/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.33039/ami.2019.09.001" target="_blank" >10.33039/ami.2019.09.001</a>

Result language
angličtina
Original language name
Pillai's problem with the Fibonacci and Padovan sequences
Original language description
Let (F_m)(m >= 0) and (P_n)(n >= 0) be the Fibonacci and Padovan sequences given by the initial conditions F_0 = 0, F_1 = 1, P_0 = 0, P_1 = P_2 = 1 and the recurrence formulas F_{m+2} = F_{m+1} + F_m, P_{n+3} = P_{n+1} + P_n for all m, n >= 0, respectively. In this note we study and completely solve the Diophantine equation P_n - F_m = P_{n_1} - F_{m_1} in non-negative integers (n, m, n(1), m(1)) with (n, m) not equal (n(1), m(1)).
Czech name
—
Czech description
—

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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