论文标题
模块化双曲线的规范形式，并应用于整数分解
Canonical form of modular hyperbolas with an application to integer factorization
论文作者
论文摘要
对于复合$ n $和带有$ c $不划分$ n $的奇数$ c $，计算了方程$ n+e equiv b \ equiv b \ mod c $带有$ a，b $ quadratic二子$ c $的解决方案的数量。我们与这些模块化溶液建立了直接关系以及模块化双曲线点之间的距离。此外，对于某些复合模量$ c $，提供了解决方案数量和$ c $之间商的渐近公式。最后，提出了用于使用此类溶液进行整数分解的算法。
For a composite $n$ and an odd $c$ with $c$ not dividing $n$, the number of solutions to the equation $n+a\equiv b\mod c$ with $a,b$ quadratic residues modulus $c$ is calculated. We establish a direct relation with those modular solutions and the distances between points of a modular hyperbola. Furthermore, for certain composite moduli $c$, an asymptotic formula for quotients between the number of solutions and $c$ is provided. Finally, an algorithm for integer factorization using such solutions is presented.
