The Arithmetic of Elliptic Curves
《The Arithmetic of Elliptic Curves》 · 第 282 页 · Chapter IX，Section 4「The S-Unit Equation」，Theorem 4.1
Let $S\subset M_K$ be a finite set of places and let $a,b\in K^*$. The equation $ax+by=1$ has only finitely many solutions in $S$-units $x,y\in R_S^*$.