Koley and Reddy's irreducibility conjecture for integer polynomials

Let $f=a_0+a_1x+\cdots+a_nx^n\in\mathbb Z[x]$, where $a_0=\pm p^k$ for a prime $p$ and positive integer $k$. Suppose that $a_1=a_2=\cdots=a_{q-1}=0$ for a prime $q\leq n$. Koley and Reddy's conjecture. If $p\nmid a_qa_n$, $q\nmid k$, and

$$p^k>|a_q|+|a_{q+1}|+\cdots+|a_n|,$$

then $f$ is irreducible over $\mathbb Q$. The paper states that this conjecture follows from an earlier theorem, so it is solved rather than open.