Monatshefte für Mathematik

, Volume 102, Issue 3, pp 251–257 | Cite as

On the Oesterlé-Masser conjecture

  • C. L. Stewart
  • R. Tijdeman
Article

Abstract

Letx, y andz be positive integers such thatx=y+z and ged (x,y,z)=1. We give upper and lower bounds forx in terms of the greatest squarefree divisor ofx y z.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ennola, V.: On numbers with small prime divisors. Ann. Acad. Sci. Fenn. Series AI440, 1–16 (1969).Google Scholar
  2. [2]
    Faltings, G.: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern. Invent. Math.73, 349–366 (1983).Google Scholar
  3. [3]
    Hall, Jr., M.: The diophantine equationx 3y 2=k. In: Computers in Number Theory. A.O.L. Atkin and B.J. Birch (eds.). Proc. Sci. Res. Council Atlas Symp. No. 2, Oxford 1969, pp. 173–198. London: Academic Press. 1971.Google Scholar
  4. [4]
    Masser, D. W.: Open problems. Proc. Symp. Analytic Number Th. W. W. L. Chen (ed.). London: Imperial College 1985.Google Scholar
  5. [5]
    Pillai, S. S.: On the equation 2x−3y=2X+3Y. Bull. Calcutta Math. Soc.37, 15–20 (1945).Google Scholar
  6. [6]
    Van der Poorten, A. J.: Linear forms in logarithms in thep-adic case. In: Transcendence Theory: Advances and Applications. A. Baker (ed.), pp. 29–57. London: Academic Press. 1977.Google Scholar
  7. [7]
    Barkley Rosser, J.: Then-th prime is greater thann logn. Proc. London Math. Soc. (2)45, 21–44 (1939).Google Scholar
  8. [8]
    Tijdeman, R.: On the equation of Catalan. Acta Arith29, 197–209 (1976).Google Scholar
  9. [9]
    De Weger, B. M. M.: Solving exponential diophantine equations using lattice basis reduction algorithms. Report Math Inst. University of Leiden. 1986, No. 13.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • C. L. Stewart
    • 1
  • R. Tijdeman
    • 2
  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Mathematical InstituteUniversity of LeidenLeidenThe Netherlands

Personalised recommendations