ON THE NUMBER OF SOLUTIONS OF SIMULTANEOUS PELL EQUATIONS

By Michael A. Bennett. 2006

139 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/84c81c13e56323f944e6961d13e3c205220e6a7b

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In Algebra and Number Theory

1. Clemens Fuchs
2. Alan Filipin
3. Andrej Dujella
4. Yasutsugu Fujita

In Computational Theory and Mathematics

1. Clemens Fuchs
2. Andrej Dujella
3. Yasutsugu Fujita
4. Alan Filipin

In Geometry and Topology

1. Yasutsugu Fujita
2. Clemens Fuchs
3. Alan Filipin
4. Andrej Dujella

Citations in the corpus

• The extensibility of Diophantine pairs {k−1,k+1} (2008, background): “2 in [3] is that we take f = 2 and D = 8(k2 − 1)2N , whereas in [3] f = 1 and D = 16(k2 − 1)2N”
• Effective solution of the D(-1)-quadruple conjecture (2007, methodology): “To obtain it we use the following slightly modified version of a special case of Bennett’s theorem [4] (it is also a modified version of Rickert’s theorem [35]), which was proved in [24].”
• On the size of Diophantine m-tuples (2000, methodology): “(4) We will apply the following theorem of Bennett [4] on simultaneous approximations of square roots of two rationals which are very close to 1.”
• An Absolute Bound for the Size of Diophantine m-Tuples (2001, methodology): “Now we will apply the following important and very useful result of Bennett [5].”
• There are only finitely many Diophantine quintuples (2004, methodology): “Comparing these lower bounds with upper bounds obtained from the Baker’s theory on linear forms in logarithms of algebraic numbers (a theorem of Matveev [18]) we prove Theorem 1, and comparing them with upper bounds obtained from a theorem of Bennett [5] on simultaneous approximations of algebraic n”
• Complete Solution of a Problem of Diophantus and Euler (2005, methodology): “Using this gap principle and a theorem about simultaneous approximations of square roots which are close to 1 due to Bennett, we obtain in Section 4 an upper bound for d. Comparing this upper bound with lower bounds obtained by congruence methods we show that such an extension does not exist, which ”