论文标题
好奇的正方形
Curious Squares
论文作者
论文摘要
一个奇怪的数字是一个回文数字，其基本十表示形式的表格$ a \ ldots a b \ ldots b a \ ldots a $。在本文中，我们确定所有奇怪的数字都是完美的正方形。我们的证明涉及将对此类数字的搜索减少到几个单个变量系列。从这里开始，我们以两种不同的方式完成了证明。第一种方法是基本的，尽管有些临时。第二个需要研究椭圆曲线上的积分点，并且更加系统。
A curious number is a palindromic number whose base ten representation has the form $a \ldots a b \ldots b a \ldots a$. In this paper, we determine all curious numbers that are perfect squares. Our proof involves reducing the search for such numbers to several single variable families. From here, we complete the proof in two different ways. The first approach is elementary, though somewhat ad hoc. The second entails studying integral points on elliptic curves and is more systematic.
