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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  ≥ (5 d  + 3)/9. Previous techniques required  k  &gt; 3 d /4. We also prove an entirely analogous result for  p   d   +  c  with  p  prime.

POWER-FREE VALUES OF POLYNOMIALS