Uva 10006-Carmichael Numbers（快速冪）

標籤：blog   http   ar   io   os   sp   for   on   2014   

題目連結：點擊開啟連結

題意：給一個數n，問這個數是不是Carmichael Numbers，Carmichael Numbers的定義為：一個數n如果不是素數且對於對於任意的    2=<a<n 都滿足 a^n%n=a,那麼這個數就是Carmichael Numbers，否則不是。快速冪暴力解決。

#include <algorithm>#include <iostream>#include <cstring>#include <cstdlib>#include <string>#include <cctype>#include <vector>#include <cstdio>#include <cmath>#include <queue>#include <stack>#include <map>#include <set>#define maxn 65002#define _ll __int64#define ll long long#define INF 0x3f3f3f3f#define Mod 10000007#define pp pair<int,int>#define ull unsigned long longusing namespace std;ll n;bool pri[maxn];void init(){memset(pri, 1, sizeof(pri));pri[0] = 0;pri[1] = 0;for (int i = 2; i * i <= maxn; i++) {if (pri[i]) {for (int j = i * i; j <= maxn; j += i) {pri[j] = 0;}}}}ll pow_mod(ll a, ll n, ll p){if (n == 0) {return 1;}ll ans = pow_mod(a, n / 2, p);ans = ans * ans % p;if (n & 1) {ans = ans * a % p;}return ans;}void solve(){if (pri[n]) {printf("%d is normal.\n", n);return ;}for (ll i = 2; i < n; i++) {if (pow_mod(i, n, n) != i) {printf("%d is normal.\n", n);return ;}}printf("The number %d is a Carmichael number.\n", n);}int main(){init();while (~scanf("%lld", &n) && n) {solve();}return 0;}

Uva 10006-Carmichael Numbers（快速冪）