Linear Equations with the Euler Totient Function

Abstract

In this paper, we investigate linear relations among the Euler function of nearby integers. In particular, we study those positive integers n such that theta(n) = theta(n -1) + (n - 2), where theta is the Euler function. We prove that they form a set of asymptotic density zero. We also show that the sum of the reciprocals of the prime values of n with the above property is a convergent series.

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Document Details

Document Type
Technical Report
Publication Date
Feb 13, 2007
Accession Number
ADA573099

Entities

People

  • Florian Luca
  • Pantelimon Stanica

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Additives (Chemicals)
  • Applied Mathematics
  • Classification
  • Composite Materials
  • Equations
  • Inequalities
  • Information Operations
  • Mathematics
  • Numbers
  • Prime Numbers
  • Real Numbers
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra