# 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

$a-2x=0$

• The set of all full squares is defined by the Diohpantine equation

$a-x^2=0$

• The set of all non-negative integers that are not full squares is defined by the Pell's equation

$(x+1)^2-a(y+1)^2=1$ provided that the unknowns $$x$$ and $$y$$ range over non-negative integers.

$(x^2-ax-a^2)^2=1$