Reprint: On the number of integers which can be represented by a binary form (1938)

  • Pál Erdős

  • Kurt Mahler


Let be a binary form of degree with integer coefficients and non-vanishing discriminant, and let be the number of different positive integers , for which has at least one solution in integers . In this paper, using Mahler's -adic generalisation of the Thue-Siegel theorem, Erdős and Mahler prove that

Reprint of the authors' paper [J. Lond. Math. Soc. 13, 134--139 (1938; Zbl 0018.34401; JFM 64.0116.01)].