ON BALANCING NUMBERS BY THE MATRIX METHOD

DOI: 10.18173/2354-1059.2025-0049

Abstract

In this study, we define a balancing B-matrix which is similar to the Fibonacci Q-matrix and the Lucas QL-matrix. Using this matrix representation, we obtain some well-known equalities and a Binet-like formula for balancing numbers. Moreover, some arithmetic properties of balancing numbers are established.