Let Δ be an integral convex polytope of dimension

*n*in a lattice

*M*, and let

*l*

_{Δ}(

*k*) be the number of lattice points in Δ dilated by a factor of the integer

*k*,

- .

*l*

_{Δ}(

*k*) can be shown to be an

*n*th-degree polynomial with rational coefficients in

*k*, called the

**Ehrhart polynomial**of the polytope Δ: