}

               else

               {

                   n/=2;  

                      cout<<"Step No."<<++cnt<<":"<<2*n<<"/2="<<n<<endl;

               }

              } while(__________);           //  （3）

        cout<<endl;

    }

       return 0;

}

3．四方定理

This program is to verify Theorem of Four Squares.That is all natural numbers can be represented as sum of no more than 4 squares of the numbers.e.g., 123=7*7+7*7+4*4+3*3.

#include <iostream>

using namespace std;

int main()

{

    int i,j,k,l,number;

    while(1)

    {

           cout<<"Please input a number to verify(0 to quit): ";

           cin>>number;

           if(number==0)  __________;          //  （1）

           cout<<" ------ Results of verification: ------------\n";

           for(i=1;i<=number/2;i++)

             for(j=0;j<=i;j++)

              for(k=0;k<=j;k++)

                for(l=0;l<=k;l++)

                       if(__________)       //  （2）

                       {

                                cout<<number<<"="<<i<<"*"<<i<<"+"<<j<<"*"<<j<<"+"<<k<<"*"<<k<<"+"<<l<<"*"<<l<<endl;

                               goto exit;

                         }