 A typical example is the linear diophantine equation in two unknowns,

where the equation is solvable when the greatest common divisor of formula_5 divides formula_6.The values for formula_7 that satisfy this restriction are a diophantine set and the equation above is its diophantine definition.Diophantine definitions can be provided by simultaneous systems of equations as well as by individual equations because the system

is equivalent to the single equation

Sets of natural numbers, of pairs of natural numbers (or even of "n"-tuples of natural numbers) that have Diophantine definitions are called "Diophantine sets".