Integer Combinations Of Vectors

You are given a collection of n integer-valued vectors v1, v2, ..., vn (i.e. integer arrays) of some fixed dimension. An integer combination of these vectors is a vector of the form v = c1v1 + ... + cnvn where each ci is an integer. Here, the j'th component v[j] is precisely c[1]v1[j] + ... + c[n]vn[j]. Define the length of a vector x = (x[1], x[2], ..., x[n]) to be the square root of x[1]*x[1] +