 That is equivalent to saying there is an algorithm that runs forever and lists the members of "S".A set "S" is Diophantine precisely if there is some polynomial with integer coefficients "f"("n", "x"1, ..., "x""k")
such that an integer "n" is in "S" if and only if there exist some integers
"x"1, ..., "x""k"
such that "f"("n", "x"1, ..., "x""k") = 0.Conversely, every Diophantine set is computably enumerable