A note on an irreducible class of polynomials over integers

2023/03/07 by Weilin, Zhang, Pingzhi, Yuan
#11C08 #11R09 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.03605

Abstract

In this note, we prove an irreducibility criterion for the polynomial of the form f(x) = a_nxⁿ + a_n-1x^n-1 + ⋯ + a_mx^m + p^u ∈ ℤ[x], where p is a prime number, u \geqslant 1, gcd(u, m) = 1, p \nmid a_m and p^u > |a_n| + |a_n-1| + ⋯ + |a_m|. In particular, we show that the conjecture of Koley and Reddy is true.

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