# Short Integer Solution Problem with ||z||<=B

Why following constraints on $$||z||$$ are required

$$||z||<=B, B

• The Short Integer Solution problem is trivial for $\beta = q$, as the scaled basis vectors $q\vec{e}_i$ satisfy: $$f_{\mathbf{A}}(q\vec{e}_i) = \mathbf{A}q\vec{e}_i \equiv 0\bmod q$$ – Mark Jan 4 at 22:36