Rendiconti del Seminario Matematico della Università di Padova
Full-Text PDF (240 KB) | Metadata | Table of Contents | RSMUP summary
Published online: 2008-06-30
Integral Points on Certain Elliptic CurvesHui Lin Zhu and Jian Hua Chen (1) Xiamen University, Fujian, China
(2) 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
y2=(x+a)(x2+bx+c), a,b,c∈Z, b2<4c.
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.
No keywords available for this article.
Zhu Hui Lin, Chen Jian Hua: Integral Points on Certain Elliptic Curves. Rend. Sem. Mat. Univ. Padova 119 (2008), 1-20. doi: 10.4171/RSMUP/119-1