Carmichael Numbers

题意翻译

题目描述：如果对任意的 1 < x < n 都有 x^n≡x(mod n) 成立的合数n称为Carmichael Numbers .先给出一些整数n,请判断是否为Carmichael Numbers 。 输入格式：n (2<n<65000) ,输入以0结尾。 输出格式：参见样例

题目描述

[problemUrl]: https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=12&page=show_problem&problem=947 [PDF](https://uva.onlinejudge.org/external/100/p10006.pdf) ![](https://cdn.luogu.com.cn/upload/vjudge_pic/UVA10006/f3ecddabe04dc663f6dc5d5e1be62ccb301f2883.png)

输入输出格式

输入格式


![](https://cdn.luogu.com.cn/upload/vjudge_pic/UVA10006/1935e9a4656caa9775e2b8eeb0bb0984793c7d7b.png)

输出格式


![](https://cdn.luogu.com.cn/upload/vjudge_pic/UVA10006/9eaefd13aa5cfafe9474f7fa8da0d137bda9de05.png)

输入输出样例

输入样例 #1

1729
17
561
1109
431
0

输出样例 #1

The number 1729 is a Carmichael number.
17 is normal.
The number 561 is a Carmichael number.
1109 is normal.
431 is normal.