HDU - 5974 A Simple Math Problem 数论

 

 关于 k1 k2 互质的问题，可以自己手动证明一下，需要一点数学直觉。

#pragma warning(disable:4996)

#include<iostream>
#include<algorithm>
#include<bitset>
#include<tuple>
#include<unordered_map>
#include<fstream>
#include<iomanip>
#include<string>
#include<cmath>
#include<cstring>
#include<vector>
#include<map>
#include<set>
#include<list>
#include<queue>
#include<stack>
#include<sstream>
#include<cstdio>
#include<ctime>
#include<cstdlib>
#define pb push_back
#define INF 0x3f3f3f3f
#define inf 0x7FFFFFFF
#define moD 1000000003
#define pii pair<ll,ll>
#define eps 1e-8
#define equals(a,b) (fabs(a-b)<eps)
#define bug puts("bug")
#define re  register
#define fi first
#define se second
typedef  long long ll;
typedef unsigned long long ull;
const ll MOD = 1e6 + 7;
const int maxn = 3e5 +5;
const double Inf = 10000.0;
const double PI = acos(-1.0);
using namespace std;

ll gcd(ll a, ll b) {
    return b == 0 ? a : gcd(b, a % b);
}



int main() {
    ll a, b, x, y;
    while (~scanf("%lld %lld", &a, &b)) {
        ll g = gcd(a, b);
        if (a * a - 4 * g * b < 0) {
            puts("No Solution");
            continue;
        }
        ll del = sqrt(a * a - 4 * g * b);
        x = (del + a) / 2;
        y = a - x;
        if (x / gcd(x, y) * y != b) {
            puts("No Solution");
            continue;
        }
        if (x > y) swap(x, y);
        printf("%lld %lld\n", x, y);
    }
}