The size of the fundamental solutions of consecutive Pell equations.
Jacobson, Michael J.jun., Williams, Hugh C. (2000)
Experimental Mathematics
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Jacobson, Michael J.jun., Williams, Hugh C. (2000)
Experimental Mathematics
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James Mc Laughlin, Peter Zimmer (2007)
Acta Arithmetica
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Mollin, R. A. (2009)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09. This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial for real quadratic fields. As well, we complete the list of Richaud-Degert types given in [16] and show how the behaviour of the Euler-Rabinowitsch polynomials and certain continued fraction expansions come into play in...
Kell Cheng, Hugh Williams (2005)
Acta Arithmetica
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Edward B. Burger, David C. Clyde, Cory H. Colbert, Gea Hyun Shin, Zhaoning Wang (2012)
Acta Arithmetica
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S. G. Dani (2015)
Acta Arithmetica
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We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the...
E. FRANK (1969)
Mathematische Annalen
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Mahony, Louis M. (1983-1984)
Portugaliae mathematica
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Beata Rothkegel (2013)
Acta Arithmetica
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Let R be a Dedekind domain whose field of fractions is a global field. Moreover, let 𝓞 < R be an order. We examine the image of the natural homomorphism φ : W𝓞 → WR of the corresponding Witt rings. We formulate necessary and sufficient conditions for the surjectivity of φ in the case of all nonreal quadratic number fields, all real quadratic number fields K such that -1 is a norm in the extension K/ℚ, and all quadratic function fields.
Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)
Acta Arithmetica
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Xue Hai Hu, Jun Wu (2009)
Acta Arithmetica
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Takao Komatsu (2003)
Acta Arithmetica
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Boonrod Yuttanan (2012)
Acta Arithmetica
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Peter SZÜSZ, Andrew M. Rockett (1990)
Forum mathematicum
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Yann Bugeaud, Pascal Hubert, Thomas A. Schmidt (2013)
Journal of the European Mathematical Society
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We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.
Boris Adamczewski (2010)
Acta Arithmetica
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