Hdu 5615 Jam's math problem【数学】

Jam's math problem

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)

Total Submission(s): 924 Accepted Submission(s): 444

Problem Description

Jam has a math problem. He just learned factorization.
He is trying to factorize ax2+bx+c into the form of pqx2+(qk+mp)x+km=(px+k)(qx+m).
He could only solve the problem in which p,q,m,k are positive numbers.
Please help him determine whether the expression could be factorized with p,q,m,k being postive.

Input

The first line is a number T, means there are T(1≤T≤100) cases

Each case has one line,the line has 3 numbers a,b,c(1≤a,b,c≤100000000)

Output

You should output the "YES" or "NO".

Sample Input

21 6 51 6 4

Sample Output

YESNO
Hint
The first case turn $x^2+6*x+5$ into $(x+1)(x+5)$
 

题意：

给出一个一元二次方程的一般式的a，b，c 的值，问这个方程是否有整数解

题解：

数学知识：如果一个一元二次方程的判别式是一个整数的完全平方式，那么这个方程必定有整数解（也许这真是个结论吧，网上搜到的此类信息也不多）

/*一元二次方程有整数解的条件是：判别式是完全平方数或者完全平方式！ */#include<stdio.h>#include<math.h>typedef long long ll;int slove(ll a,ll b,ll c){    ll dot=b*b-4*a*c;    if(dot<0)    {        return 0;    }    ll tp=sqrt(dot*1.0);    return tp*tp==dot;}int main(){    int t;    scanf("%d",&t);    while(t--)    {        int a,b,c;        scanf("%d%d%d",&a,&b,&c);        printf("%s\n",slove(a,b,c)?"YES":"NO");    }    return 0;}