SOME LINKS OF BALANCING AND COBALANCING NUMBERS WITH PELL AND ASSOCIATED PELL NUMBERS

摘要

Links of balancing and cobalancing numbers with Pell and associated Pell numbers are established. It is proved that the n~(th) balancing number is product of the n~(th) Pell number and the n th associated Pell number. It is further observed that the sequences of balancing and cobalancing numbers are very closely related to the Pell sequence whereas, the sequences of Lucas-balancing and Lucas-cobalancing numbers constitute the associated Pell sequence. The solutions of some Diophantine equations including Pythagorean and Pythagorean-type equations are obtained in terms of these numbers.