On arithmetic functions of balancing and Lucas-balancing numbers

Utkal Keshari Dutta; Prasanta Kumar Ray

Vol. 24 No. 1 (2019)

Regular Articles

On arithmetic functions of balancing and Lucas-balancing numbers

Published 2018-07-10

Utkal Keshari Dutta
Prasanta Kumar Ray

Utkal Keshari Dutta
Sambalpur University, Sambalpur

Prasanta Kumar Ray
Sambalpur University, Sambalpur

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Abstract

For any integers $n\geq1$ and $k\geq0,$ let $\phi(n)$ and $\sigma_{k}(n)$ denote the Euler phi function and the sum of the $k$-th powers of the divisors of $n$, respectively. In this article, the solutions to some Diophantine equations about these functions of balancing and Lucas-balancing numbers are discussed.

Keywords

Eluer phi function, Divisor function, Balancing numbers, Lucas-balancing numbers

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Author Biography

Prasanta Kumar Ray

Department of Mathematics

Professor