欧拉定理

#include
#define rep(i,a,b) for(ll i=(a);i<=(b);i++)
#define per(i,a,b) for(ll i=(a);i>=(b);i--)
#define ll long long
using namespace std;
const ll N=2e6;
ll flag,mod,a,m,b;
ll read(){
    ll num=0;char ch=getchar();
    while(!isdigit(ch))ch=getchar();
    while(isdigit(ch)){
        num=1LL*num*10+ch-'0',ch=getchar();
        if(num>=mod){
            flag=1;
            num%=mod;
        }
    }
    return num;
}
ll mul(ll a,ll b,ll mod){
    ll ans=0;for(;b;b>>=1,a=(a+a)%mod)if(b&1)ans=(ans+a)%mod;return ans;
}
ll power(ll a,ll b,ll mod){
    ll ans=1;for(;b;b>>=1,a=1LL*a*a%mod)if(b&1)ans=1LL*ans*a%mod;return ans;
}

ll phi(ll n){
    int ans=n;
    rep(i,2,sqrt(n)){
        if(n%i)continue;
        ans=ans/i*(i-1);
        while(n%i==0)n/=i;
    }if(n>1)ans=ans/n*(n-1);
    return ans;
}

int main()
{
    scanf("%d%d",&a,&m);
    mod=phi(m); b=read();
    if(flag)cout<<1LL*power(a,b,m)*power(a,mod,m)%m;
    else cout<

 

[上帝与集合的正确用法]

#include
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
using namespace std;
map f;
int T,n;
inline void Print(int x){if(x>9)Print(x/10);putchar(x%10+'0');}
int power(int a,int b,int mod)
{int ans=1;for(;b;b>>=1,a=1LL*a*a%mod)if(b&1)ans=1LL*ans*a%mod;return ans;}
int phi(int n){
	int ans=n;
	rep(i,2,sqrt(n)){
		if(n%i)continue;
		ans=ans/i*(i-1);
		while(n%i==0)n/=i;
	}if(n>1)ans=ans/n*(n-1);
	return ans;
}
int F(int n){
	if(f.count(n))return f[n];
	int p=phi(n);
	return f[n]=power(2,F(p)+p,n);
}
int main()
{
	scanf("%d",&T);
	f[1]=0;
	while(T--){
		scanf("%d",&n);
		Print(F(n));puts("");
	}return 0;
}