Lagrange's Four Square Theorem/Examples

Examples of Use of Lagrange's Four Square Theorem

Example: $1$

$1$ can be trivially expressed as the sum of $4$ squares:

$1 = 1^2 + 0^2 + 0^2 + 0^2$

Example: $23$

$23$ can be expressed as the sum of $4$ squares thus:

$23 = 3^2 + 3^2 + 2^2 + 1^2$

Example: $59$

$59$ can be expressed as the sum of $4$ squares thus:

\(\ds 59\)

\(=\)

\(\ds 7^2 + 3^2 + 1^2 + 0^2\)

\(\ds \)

\(=\)

\(\ds 5^2 + 5^2 + 3^2 + 0^2\)

\(\ds \)

\(=\)

\(\ds 5^2 + 4^2 + 3^2 + 3^2\)