By using algebraic number theory method and p-adic analysis method, we find all integral points on certain elliptic curves
_y_2=(x+a)(_x_2+bx+c), a,b,_c_∈Z, b_2<4_c.
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. 1–20DOI 10.4171/RSMUP/119-1