ON CONVOLUTION OF GENERALIZED REPUNITS

Kód výsledku v 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>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

ON CONVOLUTION OF GENERALIZED REPUNITS

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

ON CONVOLUTION OF GENERALIZED REPUNITS

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International journal of pure and applied mathematics

ISSN

1311-8080

e-ISSN

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Svazek periodika

79

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

BG - Bulharská republika

Počet stran výsledku

6

Strana od-do

493-498

Kód UT WoS článku

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EID výsledku v databázi Scopus

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