POWER-FREE VALUES OF POLYNOMIALS

For irreducible polynomials of the form X^d + c we establish the expected asymptotic formula for the number of k-free integers n^d + c with n ≤ x, under the assumption that k ≥ (5d + 3)/9. Previous techniques required k > 3d/4. We also prove an entirely analogous result for p^d + c with p prime.