ON CONVOLUTION OF GENERALIZED REPUNITS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F12%3A50000604" target="_blank" >RIV/62690094:18470/12:50000604 - isvavai.cz</a>
Result on the web
<a href="http://www.ijpam.eu/contents/2012-79-3/index.html" target="_blank" >http://www.ijpam.eu/contents/2012-79-3/index.html</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
ON CONVOLUTION OF GENERALIZED REPUNITS
Original language description
The paper concentrate on properties of the generalized repunits Rn(k), where k is any nonnegative integer and n is any positive integer greater than 1. A repunit Rn is any integer written in decimal form as a string of 1´s. The term repunit was coined byBeiler in 1966. The great effort was devoted to testing of primality and finding all their prime factors. Snyder in 1982 extended the notation repunit to one in which for some integer b> 3. They are called as generalized repunits or repunits to base b and consist of a string of 1´s when written in base b. Some facts on the divisibility and primality of Rn(b) were found by Dubner in 2002 and Jaroma in 2007. In this paper some results on congruences of generalized repunits are stated. Further the generating function for generalized repunits is found, some relations for them are proved using this generating function and m-fold convolution formula is derived.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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