On the diophantine equation D₁x⁴ -D₂y² = 1
Maohua Le (1996)
Acta Arithmetica
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Maohua Le (1996)
Acta Arithmetica
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Soon-Yi Kang (1999)
Acta Arithmetica
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M. Mignotte (1998)
Acta Arithmetica
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Weiqun Hu (2000)
Acta Arithmetica
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Michael Filaseta, Ognian Trifonov (1994)
Acta Arithmetica
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Gerald Kuba (2000)
Acta Arithmetica
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Aseev, V.V., Kuzin, D.G. (2000)
Sibirskij Matematicheskij Zhurnal
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Shigeki Egami (1995)
Acta Arithmetica
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Ilka Agricola, Thomas Friedrich (1999)
Fundamenta Mathematicae
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We prove that the ring ℝ[M] of all polynomials defined on a real algebraic variety is dense in the Hilbert space , where dμ denotes the volume form of M and the Gaussian measure on M.
Hong-Quan Liu (1993)
Acta Arithmetica
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1. Introduction. The aim of this paper is to supply a still better result for the problem considered in [2]. Let A(x) denote the number of distinct abelian groups (up to isomorphism) of orders not exceeding x. We shall prove Theorem 1. For any ε > 0, , where C₁, C₂ and C₃ are constants given on page 261 of [2]. Note that 50/199=0.25125..., thus improving our previous exponent 40/159=0.25157... obtained in [2]. To prove Theorem 1, we shall proceed along the line of approach presented...