Principal divisor with one simple zero and one simple pole
= Principal divisor with one simple zero and one simple pole
If distinct points $p,q$ on a <smooth projective curve> satisfy $(f)=p-q$, then $f:C\to\mathbb P^1$ is a <finite morphism> of degree one. Such a morphism between smooth projective curves is an <isomorphism of algebraic varieties>[isomorphism], so $C$ has <geometric genus>[genus] zero. Hence no divisor $p-q$ on a curve of positive genus is principal.