Harrington's irreducibility conjecture for trinomial-like polynomials

Let $a\geq 2$ and let

$$f=\pm a(1+x^{n-1})+x^n\in\mathbb Z[x].$$

Harrington's conjecture. The polynomial $f$ is irreducible unless $f=x^2+4x+4$. The paper states that Zhang and Yuan provide an alternative proof using the Newton polygon technique, so the conjecture is solved.