Prove that for each $n\in\mathbb N$ the polynomial $(x^2+x)^{2^n}+1$ is irreducible over the polynomials with integer coefficients.
Source: Mongolian MO 2002 Teachers P2
Tags: polynomial, algebra, irreducibility
Prove that for each $n\in\mathbb N$ the polynomial $(x^2+x)^{2^n}+1$ is irreducible over the polynomials with integer coefficients.