IJPAM: Volume 79, No. 3 (2012)

ON CONVOLUTION OF GENERALIZED REPUNITS

Pavel Trojovský
Department of Mathematics
Faculty of Science
University of Hradec Králové
Rokitanského 62, 50003 Hradec Králové, CZECH REPUBLIC


Abstract. We will concentrate on properties of the generalized repunits $R_{n}(k)$, where $k$ is any nonnegative integer and $n$ is any positive integer greater than 1. 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.

Received: May 31, 2012

AMS Subject Classification: 11A51, 11A07, 11Y11

Key Words and Phrases: recurrences, repunits, generating functions, congruences

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 3