Rendiconti del Seminario Matematico della Università di Padova
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Integral Points on Certain Elliptic CurvesHui Lin Zhu and Jian Hua Chen (1) School of Mathematical Sciences, Xiamen University, 361 005, Fujian, China
(2) School of Mathematics and Statistics, Wuhan University, 430072, 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.
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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