Polynomials with roots modulo every integer

Daniel Berend, Yuri Bilu

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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.

Original languageEnglish
Pages (from-to)1663-1671
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number6
StatePublished - 1 Jan 1996


  • Congruences
  • Diophantine equations
  • Effective number theory
  • Poincaré sets

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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