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ISSN : 1226-0657

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Vol.7 No.1
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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2000, v.7 no.1, pp.27-32
Park, Joong-Soo
Park,, J. (2000). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 7(1), 27-32.
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Abstract

The quadratic fields generated by <TEX>$x^2$</TEX>=ax+1(<TEX>$\alpha\geq$</TEX>1) are studied. The regulators are relatively small and are known at one. The class numbers are relatively large and easy to compute. We shall find all the values of p, where p=<TEX>$\alpha^2$</TEX>+4 is a prime in <TEX>$\mathbb{Z}$</TEX>, such that <TEX>$\mathbb{Q}(\sprt{p})$</TEX> has class numbers 1, 3 and 5.

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quadratic fields, class number

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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