Rocky Mountain Journal of Mathematics

On the Equation $y^x\pm x^y=z^2$

Florian Luca and Maurice Mignotte

Full-text: Open access

Article information

Source
Rocky Mountain J. Math. Volume 30, Number 2 (2000), 651-661.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181070342

Digital Object Identifier
doi:10.1216/rmjm/1022009287

Mathematical Reviews number (MathSciNet)
MR1787004

Subjects
Primary: 11D61: Exponential equations
Secondary: 11D72: Equations in many variables [See also 11P55]

Keywords
Exponential diophantine equations linear forms in logarithms

Citation

Luca, Florian; Mignotte, Maurice. On the Equation $y^x\pm x^y=z^2$. Rocky Mountain J. Math. 30 (2000), no. 2, 651--661. doi:10.1216/rmjm/1022009287. https://projecteuclid.org/euclid.rmjm/1181070342.


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References

  • Y. Bugeaud and M. Laurent, Minoration effective de la distance $p$-adique entre puissances de nombres algébriques, J. Number Theory 61 (1996), 311-342.
  • M. Laurent, M. Mignotte and Y. Nesterenko, Formes linéaires en deux logarithmes et déterminants d'interpolation, J. Number Theory 55 (1995), 285-321.
  • M. Mignotte, A corollary to a theorem of Laurent-Mignotte-Nesterenko, Acta Arit. 86 (1998), 101-111.
  • P. Ribenboim, Catalan's conjecture, Academic Press, Boston, 1994.