Integral Points on Certain Elliptic Curves

  • Hui Lin Zhu

    Xiamen University, Fujian, China
  • Jian Hua Chen

    Wuhan University, Wuhan, Hubei, China


By using algebraic number theory method and p-adic analysis method, we find all integral points on certain elliptic curves

Furthermore, we can find all integer solutions of certain hyperelliptic equations

As a particular example, we give a complete solution of the equation which was proposed by Zagier

by this method. In Appendix I and Appendix II, we give the computational method of finding the fundamental unit and factorizing quadratic algebraic number in the subring of a totally complex quartic field, respectively.

Cite this article

Hui Lin Zhu, Jian Hua Chen, Integral Points on Certain Elliptic Curves. Rend. Sem. Mat. Univ. Padova 119 (2008), pp. 1–20

DOI 10.4171/RSMUP/119-1