Encyclopedia > Diophantine set

  Article Content

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.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article

... 2nd century - 3rd century - 4th century Decades: 190s 200s 210s 220s 230s - 240s - 250s 260s 270s 280s 290s Years: 237 238 239 240 241 - 242 - ...

This page was created in 36.9 ms