 This question arose from consideration of the Mordell equation in the theory of integer points on elliptic curves.The original version of Hall's conjecture, formulated by Marshall Hall, Jr. in 1970, says that there is a positive constant "C" such that for any integers "x" and "y" for which "y"2 ≠ "x"3,

Hall suggested that perhaps "C" could be taken as 1/5, which was consistent with all the data known at the time the conjecture was proposed.Danilov showed in 1982 that the exponent 1/2 on the right side (that is, the use of |"x"|1/2) can't be replaced by any higher power