hdu 4335（数论）

降幂公式
A ^ x = A ^ (x % Phi(C) + Phi(C) ) (mod C) （x>=Phi(C)）

typedef unsigned long long ull;
const double eps = 1e-6;

ull get_eular(ull m) {
	ull ret = 1;
	for (ull i = 2; i * i <= m; ++i) {
		if (m % i == 0) {
			ret *= i - 1;
			m /= i;
			while (m % i == 0) {
				m /= i;
				ret *= i;
			}
		}
	}
	if (m > 1)
		ret *= m - 1;
	return ret;
}

ull qmod(ull a, ull b, ull mod) {
	ull ret = 1;
	while (b) {
		if (b & 1)
			ret = (ret * a) % mod;
		a = (a * a) % mod;
		b >>= 1;
	}
	return ret;
}

ull b, p, m, ring[100005];

int main() {
	int t, cas = 0;	
	scanf("%d", &t);
	while (t--) {
		scanf("%I64u%I64u%I64u", &b, &p, &m);
		printf("Case #%d: ", ++cas);
		if (p == 1) {
			if (m == 18446744073709551615ULL)
				printf("18446744073709551616\n");
			else printf("%I64u\n", m + 1);
			continue;
		}

		ull i = 0, phi = get_eular(p), fac = 1, ans = 0;
		//第一个环节， n! < phi(p)
		for (i = 0; i <= m && fac <= phi; ++i) {
			if (qmod(i, fac, p) == b)
				ans++;
			fac *= i + 1;
		}
		fac = fac % phi;
		//第二个环节， n ^ (n! % phi(p) + phi(i) )直到指数固定为phi(p)
		for (; i <= m && fac; ++i) {
			if (qmod(i, fac + phi, p) == b)
				ans++;
			fac = (fac * (i + 1) % phi);
		}

		if (i <= m) {
			ull cnt = 0;
			// 打表一个循环
			for (int j = 0; j < p; ++j) {
				ring[j] = qmod(i + j, phi, p);
				if (ring[j] == b)
					cnt++;
			}

			ull idx = (m - i + 1) / p;
			ans += cnt * idx;
			ull remain = (m - i + 1) % p;
			for (int j = 0; j < remain; ++j)
				if (ring[j] == b)
					ans++;
		}

		printf("%I64u\n", ans);
	}
	
	return 0;
}