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Polynomials with roots modulo every integer. (English) Zbl 1055.11523

Summary: 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.

MSC:

11R09 Polynomials (irreducibility, etc.)
11R45 Density theorems
11D61 Exponential Diophantine equations
11U05 Decidability (number-theoretic aspects)
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