New proofs of some theorems for binomial transform and Fibonacci powers

2022/03/26 by R. Sanchez Peregrino, Peregrino, R. Sanchez
Mathematics · #Analytic Number Theory Research #Mathematics and Applications #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2204.02194

Abstract

Our aim in writing this paper is to answer to both V. E. Hoggatt, JR \citehogg and Wessner\citewess on the next question: find ∑_k=0ⁿ\binomnkF_[k]^p, for the case p≡ 1 mod 4 and p≡ 3 mod 4. \par The case p≡ 0 mod 4 and p≡ 2 mod 4, Wessner has given an answer. In particular, we give another presentation, another proof of the paper of Wessner. Our method use, essentially, the paper of Boyadzhiev\citeboy

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