On Pell, Pell-Lucas, and balancing numbers

Abstract

Abstract In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the integer sequences mentioned in the text.

Keywords

• Pell numbers
• Pell-Lucas numbers
• balancing numbers
• perfect squares
• divisibility properties
• Pell equations