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Diophantine set

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.

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