Some algebraic relations on balancing numbers

Abstract

In this work we deduce some new algebraic relations on ba. lancing numbers and their relationships with Pell, Pell-Lucas and oblong numbers. Also we formulate the sums of balancing, Pell and Pell-Lucas numbers in terms of balancing numbers. We deduce some relations on perfect squares, Pythagorean triples, congruent numbers, circulant matrices and spectra] norms involving balancing numbers. Later, we formulate the integer solutions of some specific Pell equations via terms of balancing numbers. © 2015 Utilitas Mathematics.