Divisor class on the projective line
= Divisor class on the projective line
Every degree-zero divisor on the <projective line> is principal. Indeed, if $D=\sum_i a_ip_i$ and $L_i$ is a homogeneous linear form vanishing at $p_i$, then $\sum_i a_i=0$ makes
$$
f=\prod_iL_i^{a_i}
$$
a degree-zero rational function with $(f)=D$. Consequently, two divisors on $\mathbb P^1$ are linearly equivalent exactly when they have the same degree.