  This paper deals with the fully parabolic attraction-repulsion chemotaxis
system \begin{align*} u_t=\Delta u-\chi\nabla \cdot (u\nabla v)+\xi
\nabla\cdot(u \nabla w), \quad v_t=\Delta v-v+u, \quad w_t=\Delta w-w+u, \quad
x \in \Omega,\ t>0 \end{align*} under homogeneous Neumann boundary conditions
and initial conditions, where $\Omega$ is an open ball in $\mathbb{R}^n$ ($n
\ge 3$), $\chi, \xi>0$ are constants. When $w=0$, finite-time blow-up in the
corresponding Keller-Segel system has already been obtained. However,
finite-time blow-up in the above attraction-repulsion chemotaxis system has not
yet been established except for the case $n=3$. This paper provides an answer
to this open problem by using a transformation which leads to a system
presenting structural advantages respect to the original.
