138-Street Numbers // brute force or equation solving

Bs first. You can create a table before submitting this question.

At the beginning, there was a problem with binary writing. I first found n and then m. In fact, we need to first find m and then find n.

Another solution is to solve the equation and solve the Pell Equation.

You must first find the expression for both brute force and equation solving. N * (n + 1)/2 = x * (x + 1)/2-n * (n + 1) + n; n * n/2 = x * x + x. Then it is transformed into a standard Pel equation, and then solved by recursion.

The following is the binary code:

#include<iostream>#include<cstdio>using namespace std;const int n=~(unsigned int)0/2;int main(){    int t=0;    for(long long i=6;i<n&&t<=10;i++)    {        long long min=1;        long long max=i+1;        long long mid;        while(min<=max)        {            mid=(min+max)/2;            if(mid*mid*2==i*(i+1))            {                printf("%10lld%10lld\n",mid,i);                t++;                break;            }            else if(mid*mid*2>i*(i+1)) max=mid-1;            else min=mid+1;        }    }    return 0;}

It takes about 3 minutes to obtain 10 groups of solutions. .....

The code for solving the equation is as follows:

#include<iostream>#include<cstdio>using namespace std;int main(){    int x3,y3;    for(int x1=1,y1=1,x2=1,y2=1,t=0;t<10;t++)    {        x3=(2*x1+1)*(2*x2+1)+8*y1*y2;        y3=(2*x1+1)*y2+y1*(2*x2+1);        printf("%10d%10d\n",y3,(x3-1)/2);        x2=(x3-1)/2;        y2=y3;    }    return 0;}