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Quadratic Non-Residues and Prime-Producing Polynomials

Published online by Cambridge University Press:  20 November 2018

R. A. Mollin  and
H. C. Williams
R. A. Mollin
Affiliation:
Mathematics Dept., University of Calgary, Calgary, Alberta, T2N 1N4, Canada
H. C. Williams
Affiliation:
Computer Science Dept., University of Manitoba, Winnipeg, Manitoba, R3T2N2, Canada
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Abstract

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We will be looking at quadratic polynomials having positive discriminant and having a long string of primes as initial values. We find conditions tantamount to this phenomenon involving another long string of primes for which the discriminant of the polynomial is a quadratic non-residue. Using the generalized Riemann hypothesis (GRH) we are able to determine all discriminants satisfying this connection.

Keywords

12A2012A25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 474 - 478
Copyright
Copyright © Canadian Mathematical Society 1989

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