Generalized arithmetic progression

In mathematics, a multiple arithmetic progression, generalized arithmetic progression, or k -dimensional arithmetic progression, is a set of integers constructed as an arithmetic progression is, but allowing several possible differences. So, for example, we start at 17 and may add a multiple of 3 or of 5, repeatedly. In algebraic terms we look at integers

: a + mb + nc + ...

where a , b , c and so on are fixed, and m , n and so on are confined to some ranges

:0 ≤ m ≤ M ,

and so on, for a finite progression. The number k , that is the number of permissible differences, is called the dimension of the generalized progression.