Greatest common divisors of shifted balancing numbers

Authors

  • Prasanta Kumar Ray Department of Mathematics, International Institute of Information and Technology (IIIT) , Bhubaneswar, Odisha,

DOI:

https://doi.org/10.5269/bspm.v35i3.26093

Keywords:

Balancing numbers, Lucas-balancing numbers, Balancing-like sequences, Shifted balancing numbers

Abstract

It is well known that the successive balancing numbers are relatively prime. Let for all integers a, sn(a) denotes the greatest common divisor of the shifted balancing numbers of the form sn(a) = gcd(Bn ô€€€ a; Bn+1 ô€€€ 6a).
In this study, we will show that fsn(1)g is unbounded whereas fsn(a)g is
bounded for a 6= 1.

Author Biography

  • Prasanta Kumar Ray, Department of Mathematics, International Institute of Information and Technology (IIIT) , Bhubaneswar, Odisha,

    Assistant Professor

    Department of Mathematics

     

Downloads

Published

2016-10-25

Issue

Vol. 35 No. 3 (2017)

Section

Research Articles

License

When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).

The journal utilize the Creative Common Attribution (CC-BY 4.0).

 

Crossref
Scopus
Google Scholar
Europe PMC