  In this article we study the nonlocal equation \begin{align}
  (-\Delta)^{\frac{n}{2}}u=(n-1)!e^{nu}\quad \text{in $\mathbb{R}^n$},
\quad\int_{\mathbb{R}^n}e^{nu}dx<\infty, \notag \end{align} which arises in the
conformal geometry. Inspired by the previous work of C. S. Lin and L.
Martinazzi in even dimension and T. Jin, A. Maalaoui, L. Martinazzi, J. Xiong
in dimension three we classify all solutions to the above equation in terms of
their behavior at infinity.
