Abstract:
The main purpose of this paper is to study some sums
of powers of Fibonacci polynomials and Lucas polynomials, and give
several
interesting identities. Finally, using these identities we shall prove a conjecture proposed by R. S. Melham in [4].
Key Words: Fibonacci polynomials, Lucas polynomials, combinatorial method, identity, R. S. Melham's conjectures.
2000 Mathematics Subject Classification: Primary: 11B39;
Secondary: 26D10.
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