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Prime Producing Quadratic Polynomials and Class-Numbers of Real Quadratic Fields

Published online by Cambridge University Press:  20 November 2018

Stéphane Louboutin
Stéphane Louboutin*
Affiliation:
University of Caen, Caen, France
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Frobenius-Rabinowitsch's theorem provides us with a necessary and sufficient condition for the class-number of a complex quadratic field with negative discriminant D to be one in terms of the primality of the values taken by the quadratic polynomial with discriminant Don consecutive integers (See [1], [7]). M. D. Hendy extended Frobenius-Rabinowitsch's result to a necessary and sufficient condition for the class-number of a complex quadratic field with discriminant D to be two in terms of the primality of the values taken by the quadratic polynomials and with discriminant D (see [2], [7]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 2 , 01 April 1990 , pp. 315 - 341
Copyright
Copyright © Canadian Mathematical Society 1990

References

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