Polynomials with roots modulo every integer
Authors:
Daniel Berend and Yuri Bilu
Journal:
Proc. Amer. Math. Soc. 124 (1996), 1663-1671
MSC (1991):
Primary 11R09, 11R45; Secondary 11D61, 11U05
DOI:
https://doi.org/10.1090/S0002-9939-96-03210-8
MathSciNet review:
1307495
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Abstract | References | Similar Articles | Additional Information
Abstract: Given a polynomial with integer coefficients, we calculate the density of the set of primes modulo which the polynomial has a root. We also give a simple criterion to decide whether or not the polynomial has a root modulo every non-zero integer.
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Additional Information
Daniel Berend
Affiliation:
Department of Mathematics and Computer Science, Ben-Gurion University, Beer Sheva 84105, Israel
Email:
berend@black.bgu.ac.il
Yuri Bilu
Affiliation:
Department of Mathematics and Computer Science, Ben-Gurion University, Beer Sheva 84105, Israel and Université Bordeaux 2, Mathématiques Stochastiques, BP26, F-33076 Bordeaux Cedex, France
Address at time of publication:
Max Planck Institute for Mathematics, Gottfried Claren Str. 26, 53225 Bonn, Germany
Email:
yuri@cfgauss.uni-math.gwdg.de
DOI:
https://doi.org/10.1090/S0002-9939-96-03210-8
Keywords:
Diophantine equations,
congruences,
effective number theory,
Poincar\'{e} sets
Received by editor(s):
March 7, 1994
Received by editor(s) in revised form:
November 28, 1994
Communicated by:
William W. Adams
Article copyright:
© Copyright 1996
American Mathematical Society