On arithmetic functions of balancing and Lucas-balancing numbers
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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PDFISSN: 1331-0623 (Print), 1848-8013 (Online)