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Solvability of the diophantine equation x2 − Dy2 = ± 2 and new invariants for real quadratic fields

Published online by Cambridge University Press:  22 January 2016

Hideo Yokoi
Hideo Yokoi*
Affiliation:
Graduate School of Human Informatics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan
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In our recent papers [3, 4, 5], we defined some new D-invariants for any square-free positive integer D and considered their properties and interrelations among them. Especially, as an application of it, we discussed in [5] the characterization of real quadratic field Q() of so-called Richaud-Degert type in terms of these new D-invariants.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 134 , June 1994 , pp. 137 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

[1] Perron, O., Die Lehre von den Kettenbruchen, Chelsea Publ. Comp., 1929.Google Scholar
[2] Takagi, T., Syoto-sesuron-kogi (Japanese), Kyoritu Publ. Comp., 1953.Google Scholar
[3] Yokoi, H., Some relations among new invariants of prime number p congruent to 1 mod 4, Advances in Pure Math., 13 (1988), 493–501.Google Scholar
[4] Yokoi, H., The fundamental unit and bounds for class numbers of real quadratic fields, Nagoya Math. J., 124 (1991), 181–197.Google Scholar
[5] Yokoi, H., New invariants and class number problem in quadratic fields, Nagoya Math. J., 132 (1993), 175–197.Google Scholar