Fibonacci sums and divisibility properties

2023/12/03 by Kunle Adegoke, Robert Frontczak, Adegoke, Kunle +1 · 1 citation
Mathematics · Physics and Astronomy · #11B37 #11B39 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.02223

openalex publication_date 2023/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Further Extensions of Sury's Identity

Related

• Binomial Fibonacci Power Sums
• Binomial sum relations involving Fibonacci and Lucas numbers
• Relations between Chebyshev, Fibonacci and Lucas polynomials via trigonometric sums
• Some notes on a Fibonacci-Lucas identity
• Fibonacci Numbers and Their Lucas Coefficients