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Euler Pseudoprimes for Half of the Bases
-
Lorenzo Di Biagio
Published/Copyright:
November 30, 2012
Abstract.
We prove that an odd number n is an Euler pseudoprime for exactly one half of the admissible bases if and only if n is a special Carmichael number, that is,
for every invertible 
.
Received: 2011-05-25
Revised: 2011-11-11
Accepted: 2011-11-18
Published Online: 2012-11-30
Published in Print: 2012-12-01
© 2012 by Walter de Gruyter Berlin Boston
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- Preface to the John Selfridge Memorial Issue
- Numbers with Integer Complexity Close to the Lower Bound
- On a Conjecture Regarding Balancing with Powers of Fibonacci Numbers
- Perfect Powers with Few Ternary Digits
- On Mullin's Second Sequence of Primes
- Log-Sine Evaluations of Mahler Measures, II
- On Odd Perfect Numbers and Even 3-Perfect Numbers
- Euler Pseudoprimes for Half of the Bases
- Odd Incongruent Restricted Disjoint Covering Systems
- Cubes in {0,1,...,n}3
- Sierpiński Numbers in Imaginary Quadratic Fields
- On a Partition Problem of Canfield and Wilf
- The 392 Problem
- Artin's Primitive Root Conjecture – A Survey
- Prime-Perfect Numbers
- Explicit Solutions of Certain Systems of Pell Equations
- The Search for Aurifeuillian-Like Factorizations
- Some Monoapparitic Fourth Order Linear Divisibility Sequences
- A Note from the Editors
Articles in the same Issue
- Masthead
- Preface to the John Selfridge Memorial Issue
- Numbers with Integer Complexity Close to the Lower Bound
- On a Conjecture Regarding Balancing with Powers of Fibonacci Numbers
- Perfect Powers with Few Ternary Digits
- On Mullin's Second Sequence of Primes
- Log-Sine Evaluations of Mahler Measures, II
- On Odd Perfect Numbers and Even 3-Perfect Numbers
- Euler Pseudoprimes for Half of the Bases
- Odd Incongruent Restricted Disjoint Covering Systems
- Cubes in {0,1,...,n}3
- Sierpiński Numbers in Imaginary Quadratic Fields
- On a Partition Problem of Canfield and Wilf
- The 392 Problem
- Artin's Primitive Root Conjecture – A Survey
- Prime-Perfect Numbers
- Explicit Solutions of Certain Systems of Pell Equations
- The Search for Aurifeuillian-Like Factorizations
- Some Monoapparitic Fourth Order Linear Divisibility Sequences
- A Note from the Editors
