Greatest common divisors of shifted balancing numbers

Prasanta Kumar Ray

doi:10.5269/bspm.v35i3.26093

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 􀀀 a; Bn+1 􀀀 6a).
In this study, we will show that fsn(1)g is unbounded whereas fsn(a)g is
bounded for a 6= 1.

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Author Biography

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

Assistant Professor

Department of Mathematics