View source for Matiyasevich theorem/Examples of Diophantine sets

Here are some simple examples of Diophantine sets.

* The set of all even non-negative integers is defined by the Diohpantine equation
:<math>a-2x=0 </math>

* The set of all full squares is defined by the Diohpantine equation
:<math>a-x^2=0 </math>

* The set of all non-negative integers that are not full squares  is defined by the [http://en.wikipedia.org/wiki/Pell's_equation Pell's  equation]
:<math>(x+1)^2-a(y+1)^2=1 </math>
provided that the unknowns <math>x</math> and <math>y</math> range over non-negative integers.

* The set of all [http://en.wikipedia.org/wiki/Fibonacci_number Fibonacci numbers] is defined by the Diophantine equation
:<math>(x^2-ax-a^2)^2=1 </math>