Orders in quadratic fields, III

Mollin, R. A.

doi:10.3792/pjaa.70.176

Proc. Japan Acad. Ser. A Math. Sci.

1994

DOI: 10.3792/pjaa.70.176

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Orders in quadratic fields, III

R. A. Mollin¹

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Cited by 6 publications

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“…Diophantine equations and class numbers. Before presenting our first main result, we state a key lemma which we proved in [7] (for arbitrary complex quadratic orders). LEMMA Proof.…”

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confidence: 99%

Solutions of Diophantine equations and divisibility of class numbers of complex quadratic fields

Mollin¹

1996

Glasgow Math. J.

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1. Introduction. We show how the solution to certain diophantine equations involving the discriminant of complex quadratic fields leads to the divisibility of the class numbers of the underlying fields. This not only generalizes certain results in the literature such as [2], [4]-[6] but also shows why certain hypotheses made in these results are actually unnecessary since, as our criteria demonstrate, these hypotheses are forced by the solution of the diophantine equations involved. Our methods are based only on the most elementary properties of a principal ideal in a complex quadratic field.

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“…Diophantine equations and class numbers. Before presenting our first main result, we state a key lemma which we proved in [7] (for arbitrary complex quadratic orders). LEMMA Proof.…”

mentioning

confidence: 99%

Solutions of Diophantine equations and divisibility of class numbers of complex quadratic fields

Mollin¹

1996

Glasgow Math. J.

Self Cite

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On an Elementary Approach to the Lebesgue–nagell Equation

Mollin¹

2005

Int. J. Number Theory

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Orders in quadratic fields, IV

Mollin¹

1995

Proc. Japan Acad. Ser. A Math. Sci.

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Orders in quadratic fields, III

Cited by 6 publications

References 7 publications

Solutions of Diophantine equations and divisibility of class numbers of complex quadratic fields

Solutions of Diophantine equations and divisibility of class numbers of complex quadratic fields

On an Elementary Approach to the Lebesgue–nagell Equation

Orders in quadratic fields, IV

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