List of numbers

[Quantum++]

How can I find/program a list of:
We only operate with natural numbers.

1. The prime numbers < 10 000
2. x = a^2 + b^2 < 10 000
3. x = a^3 + b^3 < 10 000
4. x = a^2 + b^2 + c^2 < 10 000
5. x = a^3 + b^3 + c^3 < 10 000

Thank you.

[julien]

You could write such a program easily:
1. Use Eratosthene's sieve
2 and following: bound the values of a, b, c (obvious bounds) and test for all the possibilities within your boundaries

[Xitami]

Code: Select all

void q2(int x){
   int a,b;
   for(a=1;a<=71;a++)    //2*71^2 <= 10'000
      for(b=a;b<=71;b++)
         if (a*a+b*b==x)
            printf("%d %d\n",a,b);
}

[Xitami]

Code: Select all

#define N 10000
main() {
        int i, j, t[N]={0,0,1};
        for( i=3; i<N; i++ )
                t[i]=2;
        for( i=2; i<N; i++ )
                for( j=i+1; j<N; j++ )
                        t[j] = (t[j]*i) % j;
        for( i=0; i<N; i++ )
                if(t[i])
                        printf("%d ", i); }

[julien]

This algorithm was improved over the years