# Irreducible polynomials of degree 144

Find the number of monic irreducible integer polynomials $$f(x)$$ of degree $$144$$ such that $$f(x)$$ divides $$f(x^2)$$.

Details and assumptions

A polynomial is monic if its leading coefficient is 1. For example, the polynomial $$x^3 + 3x - 5$$ is monic but the polynomial $$-x^4 + 2x^3 - 6$$ is not.

An irreducible integer polynomial is irreducible over the integers. For example, $$x^3-2$$ is irreducible over the integers, but reducible over the reals (and complex) numbers.

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