In this note, we prove an irreducibility criterion for the polynomial of the form $f(x) = a_{ n}x^{ n} + a_{ n-1}x^{ n-1} + \cdots + a_{ m}x^{ m} + p^{ u} \in \mathbb{ Z}[x]$, where $p$ is a prime number, $u \geqslant 1$, $\gcd(u, m) = 1$, $p \nmid a_{ m}$ and $p^{ u} > |a_{ n}| + |a_{ n-1}| + \cdots + |a_{ m}|$. In particular, we show that the conjecture of Koley and Reddy is true.
Categories: math.NT