Period of balancing numbers modulo product of consecutive Lucas-balancing numbers

Abstract

The period of the balancing numbers modulo m, denoted by π(m), is the least positive integer l such that {Bl, Bl+1} ≡ {0, 1} (mod m), where Bl denotes the l-th balancing number. In the present study, we examine the periods of the balancing numbers modulo a product of consecutive Lucas-balancing numbers. MSC 2010. 11B39.