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
- The set of all full squares is defined by the Diohpantine equation
- 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.
- The set of all Fibonacci numbers is defined by the Diophantine equation