Lagrange and 2017

Computer Science Level 4

Lagrange's four square theorem says that every non-negative integer $n$ can be expressed as a sum of 4 perfect squares .

For example: $2017= 18^2+ 21^2+ 24^2 +26^2$ .

How many quadruples of positive integers $(a,b,c,d)$ such that $a\le b\le c\le d$ and $a^2+b^2+c^2+d^2=2017$ ?

The answer is 49.

1 solution

Rushikesh Jogdand
Feb 20, 2017

#include <stdio.h>
#define N 2017
int main()
{
    int count = 0;
    int a, b, c, d;
    for(a = 1; a < 45; a++)
        for(b = a; b < 45; b++)
            for(c = b; c < 45; c++)
                for(d = c; d < 45; d++)
                    if(a * a + b * b + c * c + d * d == N){
                        count += 1;
                        break;
                    }
    printf("%d", count);
}

Lagrange and 2017

The answer is 49.

1 solution

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