<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/1fm7vn.png" alt="alt text">
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/10a3i1.png" alt="alt text">
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/dv0ybw.png" alt="alt text">
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/4qcg7l.png" alt="alt text">
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/37ubg6.png" alt="alt text">
我上次最后因为写的太简略写错了一点，如图
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/z4x9s0.png" alt="alt text">
这里是（a,p1）=1 的情况, 如果 p1|a,那么
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/vz4qjx.png" alt="alt text">
是显然的, 这里因为 Carmichael 数是
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/fkjjle.png" alt="alt text">
得到的。进行素性测试时，还是 Miller-Rabin 方法更好，原因是至少 75%的数是 witness，对于几百位的数可操作性很强
最后暑假快乐！
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/wofiqx.png" alt="alt text">
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/5ld1e8.png" alt="alt text">
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/3u1ocy.png" alt="alt text">
<img src="https://pub-0be4bc99725a45ac9b3be7ebcdc45895.r2.dev/u051z2.png" alt="alt text">

数论学习笔记