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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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...
Henry Cohn (1996)
Acta Arithmetica
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Komatsu, Takao (2006)
Mathematica Pannonica
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Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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Takao Komatsu (2003)
Acta Arithmetica
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Barry R. Smith (2015)
Acta Arithmetica
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We show that for a fixed integer n ≠ ±2, the congruence x² + nx ± 1 ≡ 0 (mod α) has the solution β with 0 < β < α if and only if α/β has a continued fraction expansion with sequence of quotients having one of a finite number of possible asymmetry types. This generalizes the old theorem that a rational number α/β > 1 in lowest terms has a symmetric continued fraction precisely when β² ≡ ±1(mod α ).
Peter SZÜSZ, Andrew M. Rockett (1990)
Forum mathematicum
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James Mc Laughlin (2008)
Acta Arithmetica
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Boris Adamczewski (2010)
Acta Arithmetica
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Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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Boonrod Yuttanan (2012)
Acta Arithmetica
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