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A generalization of a Ramanujan's exercise and Fibonacci polynomials

Genki Shibukawa

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 $x^{n} - 1$.

A generalization of a Ramanujan's exercise and Fibonacci polynomials

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 .
Paper Structure (4 sections, 6 theorems, 44 equations)

This paper contains 4 sections, 6 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of Theorem \ref{['thm:main theorem']}
  4. A generalization

Key Result

Theorem 1

The polynomial $at^{2}+t-a^{-1}$ is a factor of where

Theorems & Definitions (9)

  • Theorem 1: Theorem 1.3.1 TV
  • Theorem 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Remark 6
  • Corollary 7
  • Example 8: $a=b=-1$
  • Example 10