In
mathematics, a
set S of
integers is
Diophantine precisely if there is some
polynomial with integer coefficients
f(
n,
x1,...,
xk) such that an integer
n is in
S if and only if there exist some integers
x1,...,
xk with
f(
n,
x1,...,
xk)=0. (Such a polynomial equation over the integers is also called a
Diophantine equation.)
As a consequence of Matiyasevich's theorem, a set of integers is Diophantine if and only if it is recursively enumerable.