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The 392 Problem
-
Aaron Meyerowitz
und
John Selfridge
Veröffentlicht/Copyright:
30. November 2012
Abstract.
Suppose that a is a positive non-square integer and we wish to multiply a subset of 
to form a square so that a is used and we minimize the largest number used. Now add the requirement that we must use at most f factors in forming the square. Erdős, Malouf, Selfridge, and Szekeres
conjectured that if 
, then using 
factors results in a smaller maximum than using 
factors. Their paper on this subject reduces the conjecture to the case that a is a term in a certain sequence 
, where 
grows almost as fast as 
. We give theoretical and computational results which establish the result for 
and for several infinite classes that comprise a positive proportion of the subscripts N.
Received: 2011-07-01
Revised: 2011-11-02
Accepted: 2012-01-19
Published Online: 2012-11-30
Published in Print: 2012-12-01
© 2012 by Walter de Gruyter Berlin Boston
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Artikel in diesem Heft
- 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
Artikel in diesem Heft
- 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
