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Lagrange’s four square theorem in C++
In this tutorial, we are going to learn about largrange's four square theorem.
The lagranges's four square theorem states that every natural number can be written as sum of squares of 4 numbers.
The following code finds the 4 numbers which satisfies the above condition for the given number n.
Example
Let's see the code.
#include <bits/stdc++.h>
using namespace std;
void printSquareCombinations(int n) {
for (int i = 0; i * i <= n; i++) {
for (int j = i; j * j <= n; j++) {
for (int k = j; k * k <= n; k++) {
for (int l = k; l * l <= n; l++) {
if (i * i + j * j + k * k + l * l == n) {
cout << n << " = " << i << "*" << i << " + " << j << "*" << j << " + " << k << "*" << k << " + "<< l << "*" << l << endl;
}
}
}
}
}
}
int main() {
int n = 25;
printSquareCombinations(n);
return 0;
}Output
If you run the above code, then you will get the following result.
25 = 0*0 + 0*0 + 0*0 + 5*5 25 = 0*0 + 0*0 + 3*3 + 4*4 25 = 1*1 + 2*2 + 2*2 + 4*4
Conclusion
If you have any queries in the tutorial, mention them in the comment section.
Updated on: 09-Apr-2021
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