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.
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Research supported by NSF Grant MCS 7903060.
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References
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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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