KöMaL 2019 A744

Show that for every odd integer $N>5$ there exist vectors $\mathbf{u},\mathbf{v},\mathbf{w}$ in (three-dimensional) space which are pairwise perpendicular, not parallel with any of the coordinate axes, have integer coordinates, and satisfy $|\mathbf{u}|=|\mathbf{v}|=|\mathbf{w}|=N$.