数论专题

一定要注意前提条件 ！！！！gcd(a,p)=1

#include<bits/stdc++.h>
using namespace std;
#define lowbit(x) x&(-x)
#define ll long long
map<ll,int>mp;
ll mod,b,n; 
ll ksm(ll aa,ll bb){
	ll res=1;
	while(bb){
		if(bb&1)res=res*aa%mod;
		bb>>=1;aa=aa*aa%mod;
	}
	return res;
}
ll mul(ll aa,ll bb){
	ll res=0;
	while(bb){
		if(bb&1)res=(res+aa)%mod;
		bb>>=1;
		aa=aa*2%mod;
	}
	return res;
}
void bsgs(ll,ll);
int main(){
    cin>>mod>>b>>n;
    bsgs(b,n);
	return 0;
}
void bsgs(ll a,ll b){
	ll m=sqrt(mod)+1;
	ll now=b;
	for(int i=0;i<m;i++){
		mp[now]=i;
		now=mul(now,a);
	}
	now=1;ll t=ksm(a,m);
	for(int i=1;i<=m;i++){
		now=mul(now,t);
		if(mp.count(now)){
			printf("%lld\n",i*m-mp[now]);
			return;
		}
	}
	printf("no solution\n");
}

namespace qjhz {
    typedef long long LL;
    int T, N, num;
    LL A, B;
    int a[100];
    void prime(int n) {
        num = 0;
        for (int i = 2; i*i <= n; i++) {
            if ((n%i) == 0) {
                num++;
                a[num] = i;
                while ((n%i) == 0) {
                    n /= i;
                }
            }
        }
        if (n > 1) {
            num++;
            a[num] = n;
        }
        return;
    }
    LL solve(LL r, int n) {
        prime(n);
        LL res = 0;
        for (int i = 1; i < (1 << num); i++) {
            int kk = 0;
            LL div = 1;
            for (int j = 1; j <= num; j++) {
                if (i&(1 << (j - 1))) {
                    kk++;
                    div *= a[j];
                }
            }
            if (kk % 2)
                res += r / div;
            else
                res -= r / div;
        }
        return r - res;

    }

    LL que(LL L, LL R, LL k) {
        return solve(R, k) - solve(L - 1, k);
    }
}

void slove() {
    int a, m; cin >> a >> m;
    int g = gcd(a, m);
    int L = a / g, R = (a + m - 1) / g;
    cout << qjhz::que(L, R, m / g) << endl;
}