A.I.Bonciocat, N.C. Bonciocat, and A. Zaharescu: On the irreducibility of polynomials that take a prime power value, p.41-54

Abstract:

We provide several irreducibility criteria for polynomials with integer coefficients that take a prime power value and either have one large coefficient, or have all the coefficients of modulus $1$. We also obtain upper bounds for the total number of irreducible factors of such polynomials, by studying their higher derivatives.

Key Words: Estimates for polynomial roots, prime power, irreducible polynomials.

2000 Mathematics Subject Classification: Primary: 11C08;
Secondary: 11R09.

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