Squares in arithmetic progression with at most two terms omitted
Shanta Laishram, T. N. Shorey (2008)
Acta Arithmetica
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Displaying similar documents to “The equation n(n+d) ⋯ (n+(k-1)d) = by² with ω(d) ≤ 6 or d ≤ 10¹⁰”
Squares in arithmetic progression with at most two terms omitted
Squares in products in arithmetic progression with at most one term omitted and common difference a prime power
Shanta Laishram, T. N. Shorey, Szabolcs Tengely (2008)
Acta Arithmetica
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Almost squares in arithmetic progression (II)
Anirban Mukhopadhyay, T. N. Shorey (2003)
Acta Arithmetica
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Some extensions and refinements of a theorem of Sylvester
N. Saradha, T. N. Shorey, R. Tijdeman (2002)
Acta Arithmetica
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On some arithmetic properties of polynomial expressions involving Stirling numbers of the second kind
Martin Klazar, Florian Luca (2003)
Acta Arithmetica
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Almost perfect powers in arithmetic progression
N. Saradha, T. N. Shorey (2001)
Acta Arithmetica
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Application of the explicit abc-conjecture to two Diophantine equations
N. Saradha (2012)
Acta Arithmetica
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Squares in Lehmer sequences and some Diophantine applications
Florian Luca, P. G. Walsh (2001)
Acta Arithmetica
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Squares in Lehmer sequences and the Diophantine equation Ax⁴ - By² = 2
Pingzhi Yuan, Yuan Li (2009)
Acta Arithmetica
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Solving an exponential Diophantine equation
Mario Huicochea (2010)
Acta Arithmetica
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An extension of a theorem of Euler
Noriko Hirata-Kohno, Shanta Laishram, T. N. Shorey, R. Tijdeman (2007)
Acta Arithmetica
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On the exponential Diophantine equations of the form .
Acu, Dumitru (2001)
General Mathematics
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The Diophantine equation x(x+1)...(x+(m-1)) + r = yⁿ
Yu. F. Bilu, M. Kulkarni, B. Sury (2004)
Acta Arithmetica
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Diophantine equations after Fermat’s last theorem
Samir Siksek (2009)
Journal de Théorie des Nombres de Bordeaux
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These are expository notes that accompany my talk at the 25th Journées Arithmétiques, July 2–6, 2007, Edinburgh, Scotland. I aim to shed light on the following two questions:
A note on arithmetic Diophantine series
Alexander E. Patkowski (2021)
Czechoslovak Mathematical Journal
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We consider an asymptotic analysis for series related to the work of Hardy and Littlewood (1923) on Diophantine approximation, as well as Davenport. In particular, we expand on ideas from some previous work on arithmetic series and the RH. To accomplish this, Mellin inversion is applied to certain infinite series over arithmetic functions to apply Cauchy's residue theorem, and then the remainder of terms is estimated according to the assumption of the RH. In the last section, we use...