Certain Diophantine equations involving balancing and Lucas-balancing numbers
It is well known that if x is a balancing number, then the positive square root of 8x2 + 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 8x2 +1 = y2. In this article, we consider some Diophantine equations involving balancing and Lucas-balancing numbers and study their solutions.
balancing numbers; Lucas-balancing numbers; Diophantine equations
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ISSN 1406–2283 (print)
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