UVA No.10006 Carmichael Numbers

思路：

預處理素數判斷表+快速冪求模

#include <stdio.h>
#include <string.h>
#define LL long long

int is_prime[65010];

void init_table() // prepare the table for judging prime
{
	memset(is_prime, 1, sizeof(is_prime));
	is_prime[0] = 0;
	is_prime[1] = 0;
	for (int i = 2; i < 65000; ++i)
		if(is_prime[i])
			for (int j = 2*i; j < 65000; j += i)
				is_prime[j] = 0;
}

LL quick_pow(LL x, LL n, LL pow_num) // get (x^n)%pow_num
{
	LL res = 1;
	while(n!=0)
	{
		if(n&1)
			res = (res * x)%pow_num;
		x = (x * x)%pow_num;
		n >>= 1;
	}
	return res;
}

int main()
{
	init_table();
	LL n;
	while(scanf("%lld", &n)==1&&n)
	{
		if(is_prime[n])
		{
			printf("%d is normal.\n", n);
			continue;
		}

		int flag = 1;
		for (LL i = 2; i < n; ++i)
		{
			if(i%n != quick_pow(i, n, n))
			{
				printf("%d is normal.\n", n);
				flag = 0;
				break;
			}
		}
		if(flag)
                        printf("The number %d is a Carmichael number.\n", n);
	}
}