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Some classes of irreducible polynomials

2006
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Acta Arithmetica
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1. Introduction. Lipka [10] obtained some irreducibility criteria for integer polynomials of the form f (X) = a n X n +a n−1 X n−1 +· · ·+a 1 X +a 0 p k with a 0 a n = 0, p a prime number and k a positive integer. For instance, he proved that for fixed p, a 0 , a 1 , . . . , a n with a 0 a 1 a n = 0, f is irreducible over Q for all but finitely many positive integers k. Another criterion proved in [10] is that given integers a 0 , a 1 , . . . , a n with a 0 a n = 0, the polynomial a n X n + a

doi:10.4064/aa123-4-4
fatcat:2uzfaufhnrfoxdswd6zn3a5q6m