UVa 10006 - Carmichael Numbers
传送门
UVa 10006 - Carmichael Numbers
题意
给数字,判断是不是“Carmichael Numbers”。
思路
先筛出素数,再用快速幂取模判断是否满足条件。
代码
#include <bits/stdc++.h>
using namespace std;
#define LL long long
const int MAXN = 66000;
int vis[MAXN];
LL PowMod(LL a, LL m, LL n)
{
if (m == 1)
return a % n;
LL x = PowMod(a, m >> 1, n);
LL ans = x * x % n;
if (m & 1)
ans = ans * a % n;
return ans;
}
int main()
{
//freopen("input.txt", "r", stdin);
LL n, i;
for (i = 2; i <= MAXN; i++)
if (!vis[i])
for (LL j = i * i; j <= MAXN; j += i)
vis[j] = 1;
while (scanf("%lld", &n), n)
{
if (!vis[n])
{
printf("%lld is normal.\n", n);
continue;
}
for (i = 2; i < n; i++)
if (i != PowMod(i, n, n))
{
printf("%lld is normal.\n", n);
break;
}
if (i == n)
printf("The number %lld is a Carmichael number.\n", n);
}
return 0;
}