Suppose $k$ is a field. Invertible sheaves on $\mathbb{P}_k^1$ are of the form $\mathcal{O}_{\mathbb{P}_k^1}(D)$ for some divisor $D$. For simplicity we may assume $D=x$ for some closed point $x\in |\mathbb{P}_k^1|$. The question is to show:
$$\mathcal{O}_{\mathbb{P}_k^1}(D)\simeq \mathcal{O}_{\mathbb{P}_k^1}(\mathrm{deg}\,x)$$
as sheaves on $\mathbb{P}_k^1$, here $\mathrm{deg}\,x=[k(x):k]$, $k(x)$ being the residue field of $x$.