Show that $k$-colorings of a link are in bijection with homomorphism $\pi_1(\mathbb{R}^3\setminus L)\to D_k$

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Here $D_k$ is the group of symmetries of a regular $k$-gon. $D_k$ has $2k$ elements, the $k$ rotations through multiples of $2\pi/k$ and the $k$ reflections.

I think this is related to Wirtinger presentation of knot groups, which says that if a link $L$ has strands $a_1, ..., a_n$ and the relations associated to its crossings are $r_1, ..., r_m$, then $$\pi_1(\mathbb{R}^3\setminus L)\cong\langle a_1,...a_n|\ r_1, ..., r_m\rangle.$$

I have been getting criticism for not showing any effort, the problem is I really don't know what's going on so I am asking here on mse.