Duke Mathematical Journal

On the abc conjecture, II

C. L. Stewart and Kunrui Yu

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Let x, y, and z be coprime positive integers with x+y=z. In this paper we give upper bounds for z in terms of the greatest square-free factor of xyz.

Article information

Duke Math. J. Volume 108, Number 1 (2001), 169-181.

First available in Project Euclid: 5 August 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11D75: Diophantine inequalities [See also 11J25]
Secondary: 11J25: Diophantine inequalities [See also 11D75] 11J86: Linear forms in logarithms; Baker's method


Stewart, C. L.; Yu, Kunrui. On the abc conjecture, II. Duke Math. J. 108 (2001), no. 1, 169--181. doi:10.1215/S0012-7094-01-10815-6. http://projecteuclid.org/euclid.dmj/1091737127.

Export citation


  • A. Baker, ``Logarithmic forms and the $abc$-conjecture'' in Number Theory (Eger, Hungary, 1996), de Gruyter, Berlin, 1998, 37--.
  • C. L. Stewart and K. Yu, On the $abc$ conjecture, Math. Ann. 291 (1991), 225--230. MR 92k:11037
  • P. Vojta, Diophantine Approximations and Value Distribution Theory, Lecture Notes in Math. 1239, Springer, Berlin, 1987. MR 91k:11049
  • M. Waldschmidt, A lower bound for linear forms in logarithms, Acta Arith. 37 (1980), 257--283. MR 82h:10049
  • K. Yu, Linear forms in $p$-adic logarithms, II, Compositio Math. 74 (1990), 15--113. MR 91h:11065a
  • --. --. --. --., $p$-adic logarithmic forms and group varieties, I, J. Reine Angew. Math. 502 (1998), 29--92. MR 99g:11092
  • --. --. --. --., $p$-adic logarithmic forms and group varieties, II, Acta Arith. 89 (1999), 337--378. MR 2000e:11097

See also

  • See also: C. L. Stewart, Kunrui Yu. On the abc conjecture. Math. Ann. Vol. 291, No. 2 (1991), p. 225-230.