Magic Constant of Order 5 Magic Square/Proof 1

Theorem

The magic constant of the order $5$ magic square is $65$.

Proof

Let $M_5$ denote an order $5$ magic square

By Sum of Terms of Magic Square, the total of all the entries in $M_5$ is given by:

$T_5 = \dfrac {5^2 \paren {5^2 + 1} } 2 = \dfrac {25 \times 26} 2 = 325$

As there are $5$ rows of $M_5$, the magic constant of $M_5$ is given by:

$S_5 = \dfrac {325} 5 = 65$

$\blacksquare$