Lagrange's four-square theorem : any natural number can be represented as the sum of four integer squares
p = a02 + a12 + a22 + a32
where the four numbers a0, a1, a2, a3 are integers. For illustration, 3, 31 and 310 can be represented as the sum of four squares as follows:
3 = 12 + 12 + 12 + 02
31 = 52 + 22 + 12 + 12
310 = 172 + 42 + 22 + 12.
p = a02 + a12 + a22 + a32
where the four numbers a0, a1, a2, a3 are integers. For illustration, 3, 31 and 310 can be represented as the sum of four squares as follows:
3 = 12 + 12 + 12 + 02
31 = 52 + 22 + 12 + 12
310 = 172 + 42 + 22 + 12.
int n, t1, t2, t;
n = 23;//Your number
for (int i = (int) Math.sqrt(n / 4); i * i <= n; i++) {
t1 = n - i * i;
for (int j = (int) Math.sqrt(t1 / 3); j <= i && j * j <= t1; j++) {
t2 = t1 - j * j;
for (int k = (int) Math.sqrt(t2 / 2); k <= j && k * k <= t2; k++) {
t = (int) Math.sqrt(t2 - k * k);
if (t <= k && t * t == t2 - k * k) {
System.out.println("(" + i + "^2) + (" + j + "^2) + ("+ k + "^2) + ("+ t +"^2)");
}
}
}
}
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