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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Polynomials with roots modulo every integer
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by Daniel Berend and Yuri Bilu PDF
Proc. Amer. Math. Soc. 124 (1996), 1663-1671 Request permission

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
  • Received by editor(s): March 7, 1994
  • Received by editor(s) in revised form: November 28, 1994
  • Communicated by: William W. Adams
  • © Copyright 1996 American Mathematical Society
  • 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