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The next Pellian equation

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Analytic Number Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 899))

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Abstract

The pellian equations x2−dy2=−4 in Z or ξ2∂n2=4i in Z[i] both have similar criteria of solvability according to factors of 2 or 4 in the class number for \(\mathbb{Q}(\surd - p)\), when a prime p=d or Na. The next pellian equation leads to a tower of pellian equations whose height limits the power of 2 dividing that class number.

Research supported by NSF Grant MCS 7903060.

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References

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Author information

Authors and Affiliations

  1. Mathematics Department, City College of New York, 10031, New York, N.Y.

    Harvey Cohn

Authors
  1. Harvey Cohn
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Editor information

Marvin I. Knopp

Additional information

Affectionately dedicated to Emil Grosswald in appreciation of his enthusiasm for concrete results

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© 1981 Springer-Verlag

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Cohn, H. (1981). The next Pellian equation. In: Knopp, M.I. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096463

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  • DOI: https://doi.org/10.1007/BFb0096463

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11173-3

  • Online ISBN: 978-3-540-38953-8

  • eBook Packages: Springer Book Archive

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