uva 10831 - Gerg's Cake(勒让德符号)

题目链接：uva 10831 - Gerg's Cake

题目大意：给定a和p。p为素数，问说是否存在x，使得x2≡a%p

解题思路：勒让德记号，推断ap−12≡1%p

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
typedef long long ll;

ll pow_mod (ll a, ll n, ll mod) {
    ll ans = 1;
    while (n) {
        if (n&1)
            ans = ans * a % mod;
        a = a * a % mod;
        n /= 2;
    }
    return ans;
}

int legendre (ll a, ll p) {
    a %= p;
    if (a == 0)
        return 0;
    if (pow_mod(a, (p-1)/2, p) == 1)
        return 1;
    else
        return -1;
}

int main () {
    ll a, p;
    while (scanf("%lld%lld", &a, &p) == 2 && a != -1 && p != -1) {
        if (legendre(a, p) < 0)
            printf("No\n");
        else
            printf("Yes\n");
    }
    return 0;
}

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