\u7ed9\u4e00\u4e2a\u7d20\u6570p\uff0c\u6574\u6570k\u548ca
\u5c31x^k=a(mod p)\u7684\u6240\u6709\u6574\u6570\u89e3\u3002\u3002\u3002
\u9996\u5148\u7b97\u51fa\u539f\u6839g
\u8bbex=g^i(mod p)
\u5219\u9996\u5148\u82e5a==0(\u6211\u5c31\u662f\u5fd8\u5904\u7406\u8fd9\u4e2a\u6240\u4ee5WAN\u6b21\u56e7\u3002\u3002)\u3002\u3002\u90a3\u4e48\u7b54\u6848\u5c31\u662f0.\u3002
\u5426\u5219a=g^j(mod p)
\u90a3\u4e48g^(ik)=g^j
<=> ik=j(mod p-1)..
\u7b97\u51fa\u6240\u6709\u6ee1\u8db3\u8fd9\u4e2a\u7684i\uff0c\u4ee3\u5165\u5f97\u5230\u6240\u6709x\uff0c\u6392\u5e8f\u5c31OK\u4e86\u3002\u3002
Code\uff1a
#include <vector>
#include <algorithm>
#include <utility>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <set>
#include <map>
#include <cstring>
#include <time.h>
#define rep(i,n) for(int i=0;i<n;i++)
#define pb push_back
#define Debug(x) cout<<#x<<"="<<x<<endl;
#define tr(e,x) for(typeof(x.begin()) e=x.begin();e!=x.end();e++)
const int inf=~0U>>1,maxn=20;
using namespace std;
typedef long long ll;
ll P[maxn],m=0,p,g,k,a;
void decompose(ll x)
{
for(ll i=2;i*i<=x;i++)
if(x%i==0)
{
P[m++]=i;
while(x%i==0)x\/=i;
}
if(x>1)P[m++]=x;
}
ll ext_gcd(ll a,ll b,ll&x,ll&y)
{
if(!b){x=1;y=0;return a;}
ll tmp=ext_gcd(b,a%b,y,x);y-=x*(a\/b);
return tmp;
}
ll pow(ll x,ll e)
{
if(!e)return 1;
ll tmp=pow(x,e\/2);tmp*=tmp;tmp%=p;
if(e&1)tmp*=x,tmp%=p;
return tmp;
}
ll inv(ll x)
{
return pow(x,p-2);
}
bool IsRoot(ll a)
{
rep(i,m)
if(pow(a,(p-1)\/P[i])==1)return false;
return true;
}
void FindRoot()
{
decompose(p-1);
for(ll i=2;i<p;i++)if(IsRoot(i)){g=i;break;}
}
ll discrete_Log(ll a)
{
map<ll,ll> Map;ll M=sqrt(p)+1;
ll v=inv(pow(g,M));
ll e=1;Map[1]=0;
for(ll i=1;i<M;i++){e=e*g%p;if(!Map.count(e))Map[e]=i;}
for(ll i=0;i<M;i++)
{
if(Map.count(a))return i*M+Map[a];
a=a*v%p;
}
return -1;
}
vector<ll> Solve(ll a,ll b,ll m)
{
ll x,y,d;
d=ext_gcd(a,m,x,y);
vector<ll> A;
if(b%d)return A;
ll t=b\/d;x%=m;if(x<0)x+=m;x=x*t%m;
rep(i,d)
{
A.pb(x);
x+=m\/d;x%=m;
}
return A;
}
int main()
{
\/\/freopen("in","r",stdin);
cin>>p>>k>>a;
if(a==0){cout<<1<<endl<<0<<endl;return 0;}
FindRoot();
ll Loga=discrete_Log(a);
vector<ll> Logx=Solve(k,Loga,p-1);
cout<<Logx.size()<<endl;
vector<ll> Ans;
tr(it,Logx)
{
ll tmp=pow(g,*it);
Ans.pb(tmp);
}
sort(Ans.begin(),Ans.end());
tr(it,Ans)cout<<*it<<endl;
}<\/p>\n","protected":false},"excerpt":{"rendered":"
\u7ed9\u4e00\u4e2a\u7d20\u6570p\uff0c\u6574\u6570k\u548ca\u5c31x^k=a(mod p)\u7684\u6240\u6709\u6574\u6570\u89e3\u3002\u3002\u3002\u9996\u5148\u7b97\u51fa\u539f\u6839g\u8bbex=g^i(mod p)\u5219\u9996\u5148\u82e5a==0(\u6211\u5c31\u662f\u5fd8\u5904\u7406\u8fd9\u4e2a\u6240\u4ee5WAN\u6b21\u56e7\u3002\u3002)\u3002\u3002\u90a3\u4e48\u7b54\u6848\u5c31\u662f0.\u3002\u5426\u5219a=g^j(mod p)\u90a3\u4e48g^(ik)=g^j<=> ik=j(mod p-1)..\u7b97\u51fa\u6240\u6709\u6ee1\u8db3\u8fd9\u4e2a\u7684i\uff0c\u4ee3\u5165\u5f97\u5230\u6240\u6709x\uff0c\u6392\u5e8f\u5c31OK\u4e86\u3002\u3002Code\uff1a#include <vector>#include <algorithm>#include <utility>#include <iostream>#include <cstdio>#include <cmath>#include <cstdlib>#include <set>#include <map>#include <cstring>#include <time.h>#define rep(i,n) for(int i=0;i<n;i++)#define pb push_back#define Debug(x) cout<<#x<<"="<<x<<endl;#define tr(e,x) for(typeof(x.begin()) e=x.begin();e!=x.end();e++)const int inf=~0U>>1,maxn=20;using namespace std;typedef long long ll;ll P[maxn],m=0,p,g,k,a;void decompose(ll x){ for(ll i=2;i*i<=x;i++) if(x%i==0) { P[m++]=i; while(x%i==0)x\/=i; } if(x>1)P[m++]=x;}ll ext_gcd(ll a,ll b,ll&x,ll&y){ if(!b){x=1;y=0;return a;} ll tmp=ext_gcd(b,a%b,y,x);y-=x*(a\/b); return tmp;}ll pow(ll […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[10],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/314"}],"collection":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=314"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/314\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=314"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=314"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=314"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}