k-Balancing Numbers and Pell’s Equation of Higher Orde

Abstract

First time introduced in the year 1999, the balancing numbers are extensively studied. Each balancing number is associated with a Lucas-balancing number and are useful in the computation of balancing numbers of higher order. In this report, we study the sums of k-balancing numbers with indexes in an arithmetic sequence, say an+r for fixed integers a and r. Also an infinite family of Pell’s equations of degree n>2 are discussed.