It is shown that Dickson's Conjecture about primes in linear polynomials implies that if $f$ is a reducible quadratic polynomial with integral coefficients and non-zero discriminant then for every $r$ there exists an integer $N_r$ such that the polynomial $f(X)/N_r$ represents at least $r$ distinct primes.
Keywords:
shown dicksons conjecture about primes linear polynomials implies reducible quadratic polynomial integral coefficients non zero discriminant every there exists integer polynomial represents least distinct primes
Affiliations des auteurs :
W. Narkiewicz
1
;
T. Pezda
2
1
Institute of Mathematics Wrocław University Plac Grunwaldzki 2/4 50-384 Wrocław, Poland
2
Institute of Mathematics Wrocław University Plac Grunwaldzki 2/4 50-384 Wroc/law, Poland
@article{10_4064_cm93_1_10,
author = {W. Narkiewicz and T. Pezda},
title = {On prime values of reducible quadratic polynomials},
journal = {Colloquium Mathematicum},
pages = {151--154},
year = {2002},
volume = {93},
number = {1},
doi = {10.4064/cm93-1-10},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm93-1-10/}
}
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W. Narkiewicz; T. Pezda. On prime values of reducible quadratic polynomials. Colloquium Mathematicum, Tome 93 (2002) no. 1, pp. 151-154. doi: 10.4064/cm93-1-10
