UVA 10006 Carmichael Numbers

 UVA_10006

    这个题目可以提前把素数筛除来，然后先判断是否为素数，再用快速幂取模逐个验证a^n mod n是否为a即可。

#include<stdio.h>
#include<string.h>
#include<math.h>
#define MAXD 65010
#define MAXN 65000
int N, prime[MAXD];
int init()
{
    scanf("%d", &N);
    return N;
}
void prepare()
{
    int i, j, k = (int)sqrt(MAXN) + 1;
    memset(prime, -1, sizeof(prime));
    for(i = 2; i < k; i ++)
        if(prime[i])
            for(j = i * i; j < MAXN; j += i)
                prime[j] = 0;
}
long long int powmod(int a, int n, int m)
{
    long long int res;
    if(n == 1)
        return a % m;
    res = powmod(a, n / 2, m);
    res = (res * res) % m;
    if(n % 2)
        return (res * a) % m;
    else
        return res;
}
int check()
{
    int i, j, k;
    if(prime[N])
        return 0;
    for(i = 2; i < N; i ++)
        if(powmod(i, N, N) != i)
            return 0;
    return 1;
}
void solve()
{
    if(check())
        printf("The number %d is a Carmichael number.\n", N);
    else
        printf("%d is normal.\n", N);
}
int main()
{
    prepare();
    while(init())
        solve();
    return 0;
}