POWER-FREE VALUES OF POLYNOMIALS

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