Original scientific paper

On arithmetic functions of balancing and Lucas-balancing numbers

Utkal Keshari Dutta ; Department of Mathematics, Sambalpur University, Jyoti Vihar, Sambalpur, Odisha, India
Prasanta Kumar Ray ; Department of Mathematics, Sambalpur University, Jyoti Vihar, Sambalpur, Odisha, India

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

Euler phi function; divisor function; balancing numbers; Lucas-balancing numbers

Hrčak ID:

215151

URI

https://hrcak.srce.hr/215151

Publication date:

19.4.2019.

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