sentences:  have recently extended this by three more orders of magnitude to one quadrillion.generalized Overholt's result by showing that it would follow from the abc conjecture that
  
  has only finitely many solutions, for any given integer "A".This result was further generalized by , who showed (again assuming the abc conjecture) that the equation
  
  has only finitely many integer solutions for a given polynomial "P"("x") of degree at least 2 with integer coefficients.