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Perfect Powers with Few Ternary Digits
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Michael A. Bennett
Published/Copyright:
November 30, 2012
Abstract.
We classify all integer squares (and, more generally, q-th powers for certain values of q) whose ternary expansions contain at most three digits. Our results follow from Padé approximants to the binomial function, considered 3-adically.
Received: 2011-07-20
Accepted: 2012-03-22
Published Online: 2012-11-30
Published in Print: 2012-12-01
© 2012 by Walter de Gruyter Berlin Boston
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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
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
