Results 51 to 60 of about 3,148,152 (262)
The Diophantine equation x2+2k=yn, II
International Journal of Mathematics and Mathematical Sciences, 1999 New results regarding the full solution of the diophantine equation x2+2k=yn in positive integers are obtained. These support a previous conjecture, without providing a complete proof.
J. H. E. Cohn
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, 2016 *e-mail: r.smolenski@iee.uz.zgora.pl Abstract. The assurance of the electromagnetic compatibility of sensitive smart metering systems and power electronic converters, which introduce high-level electromagnetic interference is important factor ...
J. Bojarski +3 more
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The Davenport–Heilbronn method: 80 years on
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.
Tim Browning
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The diophantine equation x2+3m=yn
International Journal of Mathematics and Mathematical Sciences, 1998 The object ofthis paper is to prove the following.
S. Akhtar Arif, Fadwa S. Abu Muriefah
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On the exponential Diophantine equation mx+(m+1)y=(1+m+m2)z
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.
Alan Murat
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Note on a paper "An Extension of a Theorem of Euler" by Hirata-Kohno et al
, 2007 In this paper we extend a result of Hirata-Kohno, Laishram, Shorey and Tijdeman on the Diophantine equation $n(n+d)...(n+(k-1)d)=by^2,$ where $n,d,k\geq 2$ and $y$ are positive integers such that $\gcd(n,d)=1.
Tengely, Szabolcs
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The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
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On the Diophantine equation $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{3p}$
AIMS Mathematics, 2017 In the present paper we obtained all positive integer solutions of some diophantine equations related to unit fraction.
Xiaodan Yuan, Jiagui Luo
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The Polynomial Solutions of Quadratic Diophantine Equation X2−ptY2+2KtX+2ptLtY = 0
Journal of Mathematics, 2021 In this study, we consider the number of polynomial solutions of the Pell equation x2−pty2=2 is formulated for a nonsquare polynomial pt using the polynomial solutions of the Pell equation x2−pty2=1.
Hasan Sankari, Ahmad Abdo
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On a Diophantine equation with prime variables
AIMS Mathematics, 2021 Let $ [\alpha] $ denote the integer part of the real number $ \alpha $, $ N $ be a sufficiently large integer and $ (\kappa, \lambda) $ be the exponent pair.
Jing Huang, Ao Han, Huafeng Liu
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