Reprint: On the rational points on curves of genus one (1934)

Abstract

Let $f(x,y)$ be an irreducible polynomial with rational coefficients and suppose that $f(x,y)=0$ defines a curve of genus one with infinitely many rational points $(x,y)$ lying on it. In this paper, Mahler shows that given a finite set $S$ of prime numbers, there are only finitely many rational points $(x,y)$ on the curve such that $x$ or $y$ has all its prime factors in $S$.

Reprint of the author's paper [J. Reine Angew. Math. 170, 168--178 (1934; Zbl 0008.20002; JFM 60.0159.03)].