When Do the Fibonacci Invertible Classes Modulo M Form a Subgroup?

Abstract

In this paper, we look at the invertible classes modulo M representable as Fibonacci numbers and we ask when these classes, say FM, form a multiplicative group. We show that if M itself is a Fibonacci number, then M < or = 8 if M is a Lucas number, then M < or = 7. We also show that if x > or = 3, the number of M < or = x such that FM is a multiplicative subgroup is O(x/(log x) exp 1/8).

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2012
Accession Number
ADA616421

Entities

People

  • Aynur Yalciner
  • Florian Luca
  • Pantelimon Stanica

Organizations

  • Naval Postgraduate School

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DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Computations
  • Differential Equations
  • Equations
  • Inequalities
  • Information Operations
  • Mathematical Analysis
  • Mathematics
  • Numbers
  • Polynomials
  • Quadratic Equations
  • Rational Numbers
  • Schools
  • Sequences
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Fields of Study

  • Mathematics

Readers

  • Battery Technology and Engineering
  • Calculus or Mathematical Analysis
  • Operations Research