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

  • Kurt Mahler


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

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