Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 186416, 4 pages
http://dx.doi.org/10.1155/2014/186416
Research Article

On the Odd Prime Solutions of the Diophantine Equation

School of Mathematics, Northwest University, Xi’an, Shaanxi 710127, China

Received 16 May 2014; Accepted 7 July 2014; Published 13 July 2014

Academic Editor: Jinde Cao

Copyright © 2014 Yuanyuan Deng and Wenpeng Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Luca and M. Mignotte, “On the equation yx±xy=z2,” The Rocky Mountain Journal of Mathematics, vol. 30, no. 2, pp. 651–661, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. M. Le, “On the Diophantine equation yx-xy=z2,” The Rocky Mountain Journal of Mathematics, vol. 37, no. 4, pp. 1181–1185, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. Y. N. Liu and X. Y. Guo, “A diophantine equation and its integer solutions,” Acta Mathematica Sinica, vol. 53, no. 5, pp. 853–856, 2010. View at Google Scholar · View at MathSciNet
  4. Z. Zhang and P. Yuan, “On the Diophantine equation axy+byz+czx=0,” International Journal of Number Theory, vol. 8, no. 3, pp. 813–821, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. Z.-F. Zhang, J.-G. Luo, and P.-Z. Yuan, “On the diophantine equation xy+yx=zz,” Chinese Annals of Mathematics, Series A, vol. 34A, no. 3, pp. 279–284, 2013. View at Google Scholar
  6. L.-G. Hua, An Introduction to Number Theory, Science Press, Beijing, China, 1979. View at MathSciNet
  7. A. J. van der Poorten, H. J. J. te Riele, and H. C. Williams, “Computer verification of the Ankeny-Artin-Chowla Conjecture for all primes less than 100 000 000 000,” Mathematics of Computation, vol. 70, pp. 1311–1328, 2001. View at Publisher · View at Google Scholar
  8. M.-H. Le, “On the number of solutions to the Diophantine equation x2-D=pn,” Acta Mathematica Sinica, vol. 34, no. 3, pp. 378–387, 1991. View at Google Scholar · View at MathSciNet