In
mathematics, a
set S of
integers 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} with
f(
n,
x_{1},...,
x_{k})=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.
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