A generalization of a Ramanujan's exercise and Fibonacci polynomials

2024/03/10 by Genki Shibukawa, Shibukawa, Genki
Mathematics · #11B39 #11B83 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical orthogonal polynomials #Combinatorics #FOS: Mathematics #Fibonacci number #Fibonacci polynomials #Generalization #Mathematical Inequalities and Applications #Mathematical analysis #Mathematics #Number Theory (math.NT) #Orthogonal polynomials #Pure mathematics #Ramanujan's sum

paper · pdf · doi:10.48550/arxiv.2403.06263

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a generalization of a Ramanujan's exercise for high school students. Our results can be regarded as a variation of the factorization formula of xⁿ - 1.

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