Squarefree values of quartics and power-free values of polynomials
We prove that every irreducible integer quartic with no fixed prime-square divisor takes squarefree values with the predicted positive Euler-product density. More generally, we obtain the corresponding $(d-2)$-power-free density in degrees $4\le d\le8$. The proof combines number-field factorization, determinant estimates with adaptive auxiliary primes, and explicit low-degree geometry. Together with Browning's theorem for higher degrees, this gives the $(d-2)$-power-free density for every d ≥ 4.
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