On the number of rational squares at fixed distance from a fifth power
On the number of rational squares at fixed distance from a fifth power
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关于距五次方固定距离的有理平方数
DOI：
10.4064/aa125-1-7
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发表时间：
2006
期刊：
影响因子：
0.7
通讯作者：
M. Stoll
中科院分区：
文献类型：
--
作者：
M. Stoll
本文的主要结果是：当曲线C_A的雅可比矩阵的Mordell-Weil秩为1时，曲线C_A上满足仿射方程y^2 = x^5 + A（其中A为无10次幂的整数）的有理点至多有7个（包括无穷远处的有理点）.当A = 18^2时，可以得到这个界限。
The main result of this note is that there are at most seven rational points (including the one at infinity) on the curve C_A with the affine equation y^2 = x^5 + A (where A is a tenth power free integer) when the Mordell-Weil rank of the Jacobian of C_A is one. This bound is attained for A = 18^2.