Polynomials with roots modulo every integer

Berend, Daniel; Bilu, Yuri

doi:10.1090/S0002-9939-96-03210-8

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: 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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