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It is well known that if x is a balancing number, then the positive square root of 8x 2 + 1 is a Lucas-balancing number. Thus, the totality of balancing number x and Lucas-balancing number y are seen to be the positive integral solutions of the Diophantine equation 8x 2 + 1 = y 2 . In this article, we consider some Diophantine equations involving balancing and Lucas-balancing numbers and study their solutions.doi:10.12697/acutm.2016.20.14 fatcat:6l652nos3zhcvat3nllh67vw4y