Rocky Mountain Journal of Mathematics

On the Diophantine Equation $y^x-x^y=z^{2^*}$

Maohua Le

Full-text: Open access

Article information

Source
Rocky Mountain J. Math. Volume 37, Number 4 (2007), 1181-1185.

Dates
First available in Project Euclid: 18 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1187453105

Digital Object Identifier
doi:10.1216/rmjm/1187453105

Mathematical Reviews number (MathSciNet)
MR2360292

Zentralblatt MATH identifier
1146.11019

Subjects
Primary: 11D61: Exponential equations

Keywords
Exponential diophantine equations

Citation

Le, Maohua. On the Diophantine Equation $y^x-x^y=z^{2^*}$. Rocky Mountain J. Math. 37 (2007), no. 4, 1181--1185. doi:10.1216/rmjm/1187453105. https://projecteuclid.org/euclid.rmjm/1187453105.


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References

  • Y. Bilu, G. Hanrot and P.M. Voutier (with Appendix by M. Mignotte), Existence of primitive divisors of Lucas and Lehmer numbers, J. Reine Angew. Math. 539 (2001), 75-122.
  • L.-K. Hua, Introduction to number theory, Springer-Verlag, Berlin, 1982.
  • M.-H. Le, Some exponential diophantine equations I: The equation $D_1x^2-D_2y^2= \la k^2$, J. Number Theory 55 (1995), 209-221.
  • F. Luca and M. Mignotte, On the equation $y^x\pm x^y=z^2$, Rocky Mountain J. Math. 30 (2000), 651-661.
  • P.M. Voutier, Primitive divisors of Lucas and Lehmer sequences, Math. Comput. 64 (1995), 869-888.