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Neither (4k2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
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Jin-Hui Fang
Published/Copyright:
June 15, 2009
Abstract
In the present paper, by employing Cilleruelo's method, we prove that neither 
(4k2 + 1) nor (2k(k – 1) + 1) is a perfect square for all n > 1, which confirms a conjecture of Amdeberhan, Medina, and Moll.
Keywords.: Perfect square; prime
Received: 2008-08-08
Revised: 2009-02-12
Accepted: 2009-03-02
Published Online: 2009-06-15
Published in Print: 2009-June
© de Gruyter 2009
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- Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
- On Newman's Conjecture and Prime Trees
- The Dying Rabbit Problem Revisited
- A Note on the q-Binomial Rational Root Theorem
- The 3x + 1 Conjugacy Map over a Sturmian Word
- The Number of Relatively Prime Subsets of {1, 2, . . . , n}
- Generalized Levinson–Durbin Sequences and Binomial Coefficients
- Neither (4k2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
- Some Arithmetic Properties of Overpartition k-Tuples
- Characterizations of Midy's Property
Articles in the same Issue
- Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
- On Newman's Conjecture and Prime Trees
- The Dying Rabbit Problem Revisited
- A Note on the q-Binomial Rational Root Theorem
- The 3x + 1 Conjugacy Map over a Sturmian Word
- The Number of Relatively Prime Subsets of {1, 2, . . . , n}
- Generalized Levinson–Durbin Sequences and Binomial Coefficients
- Neither (4k2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
- Some Arithmetic Properties of Overpartition k-Tuples
- Characterizations of Midy's Property
