The p-adic order of some Fibonomial coefficients whose entries are powers of p

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F17%3A50005611" target="_blank" >RIV/62690094:18470/17:50005611 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1134/S2070046617030050" target="_blank" >http://dx.doi.org/10.1134/S2070046617030050</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1134/S2070046617030050" target="_blank" >10.1134/S2070046617030050</a>

Result language
angličtina
Original language name
The p-adic order of some Fibonomial coefficients whose entries are powers of p
Original language description
Let (F_n) be the Fibonacci sequence. For 0<k<m+1, the Fibonomial coefficient is defined as fibm {m} {k} {k} = frac {F_ {m-k + 1} … F_ {m} } {F_1 …F_k}. In 2013, Marques, Sellers and Trojovsky proved that if p is a prime number such that p equiv -2 or 2 pmod 5, then p divides fb{p^{a+1}}{ p^a} for all integers a > 0. In 2015, Marques and Trojovsky proved that the p-adic order of fb{p^{a+1}}{ p^a} is zero for all a > 0, when p equiv -1 nebo 1 pmod 5. In this paper, we show that, for all prime p neq 5, the p-adic order of fb{p^{a+b}}{ p^a} is zero for all integers a > 0 and all even integers b>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

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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