Fibonacci sums and divisibility properties

Published 3 Dec 2023 in math.NT | (2312.02223v1)

Abstract: Based on a variant of Sury's polynomial identity we derive new expressions for various finite Fibonacci (Lucas) sums. We extend the results to Fibonacci and Chebyshev polynomials, and also to Horadam sequences. In addition to deriving sum relations, the main identities will be shown to be very useful in establishing and discovering divisibility properties of Fibonacci and Lucas numbers.

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References (1)

N. J. A. Sloane (Ed.), The On-Line Encyclopedia of Integer Sequences. Available online at https://oeis.org.

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