On the finiteness of certain Rabinowitsch polynomials. II. (English) Zbl 1033.11010

As pointed out in the review of the authors’ first paper on this topic [see J. Number Theory 94, 177–180 (2002; Zbl 0997.11024)], their results are consequences of earlier work by this reviewer and others. In this paper, the main result is an elementary consequence of a proof by Louboutin (as noted by the authors at the end of the paper).


11C08 Polynomials in number theory
11D85 Representation problems
11R29 Class numbers, class groups, discriminants


Zbl 0997.11024
Full Text: DOI


[1] Byeon, D.; Stark, H.M., On the finiteness of certain rabinowitsch polynomials, J. number theory, 94, 177-180, (2002) · Zbl 0997.11024
[2] Kim, H.K.; Leu, M.G.; Ono, T., On two conjectures on real quadratic fields, Proc. Japan acad. ser. A, 63, 222-224, (1987) · Zbl 0624.12002
[3] Mollin, R.A.; Williams, H.C., On prime valued polynomials and class numbers of real quadratic fields, Nagoya math. J., 112, 143-151, (1988) · Zbl 0629.12004
[4] R.A. Mollin, H.C. Williams, Prime producing quadratic polynomials and real quadratic fields of class number one, Theorie des nombres (Quebec, PQ, 1987), de Gruyter, Berlin, 1989, pp. 654-663.
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