poj 3696 The Luckiest number 欧拉函数在解a^x=1modm的应用

//poj 3696
//sep9
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
ll L;
ll factor[65536];

ll mul(ll x,ll y,ll p)
{
ll ret=0;
while(y){
if(y&1)
ret=(ret+x)%p;
x=(x+x)%p;
y>>=1;
}
return ret;
}

ll pow(ll x,ll n,ll m)
{
ll ret=1;
x%=m;
while(n){
if(n&1)
ret=mul(ret,x,m);
x=mul(x,x,m);
n>>=1;
}
return ret;
}

ll euler(ll n)
{
ll ret=n;
for(ll i=2;i*i<=n;++i)
if(n%i==0){
ret=ret/i*(i-1);
while(n%i==0)
n/=i;
}
if(n>1)
ret=ret/n*(n-1);
return ret;
}

ll cal()
{
ll m=L*9;
for(int i=0;i<3;++i)
if(m%2==0)
m/=2;
else
break;
if(m%2==0||m%5==0)
return 0;
ll phi=euler(m);
int idx=0;
for(ll i=1;i*i<=phi;++i)
if(phi%i==0)
factor[idx++]=i,factor[idx++]=phi/i;
sort(factor,factor+idx);
for(int i=0;i<idx;++i)
if(pow(10,factor[i],m)==1)
return factor[i];
}

int main()
{
int cases=0;
while(scanf("%I64d",&L)==1&&L){
printf("Case %d: ",++cases);
printf("%I64d\n",cal());
}
return 0;
}