论文标题
欧几里得遇见大力水平：欧几里得算法，价格为$ 2 \ times 2 $矩阵
Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ matrices
论文作者
论文摘要
Euclidean算法的类似物用于2尺寸2的平方矩阵，具有积分的非负条品和严格的积极确定性$ n $定义了有限的集合$ \ MATHCAL {r}（r}（n）欧几里德降低的矩阵，这些矩阵与$ \ \ {a，b，c，d）的元素相对应n = ab -cd，\ 0 \ le c，d <a，b \} $。在Popeye的帮助[2]关于使用晶格帆的帮助[2]我们表明，$ \ Mathcal {r}（n）$包含$ \ sum {d | n，d^2 \ ge n}（d + 1- n/d）$ elements。
An analogue of the Euclidean algorithm for square matrices of size 2 with integral non-negative entries and strictly positive determinant $n$ defines a finite set $\mathcal{R}(n)$ of Euclid-reduced matrices corresponding to elements of $\{(a, b, c, d) \in \mathbb{N}^4 | n = ab - cd,\ 0 \le c, d < a, b\}$. With Popeye's help[2] on the use of sails of lattices we show that $\mathcal{R}(n)$ contains $\sum{d|n, d^2 \ge n} (d + 1 - n/d)$ elements.
