Irreducible polynomials of degree 144

Number Theory Level 5

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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