Magic Constant of Order 4 Magic Square/Proof 1

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Theorem

The magic constant of the order $4$ magic square is $34$.


Proof

Let $M_4$ denote an order $4$ magic square

By Sum of Terms of Magic Square, the total of all the entries in $M_4$ is given by:

$T_4 = \dfrac {4^2 \left({4^2 + 1}\right)} 2 = \dfrac {16 \times 17} 2 = 136$

As there are $4$ rows of $M_4$, the magic constant of $M_4$ is given by:

$S_4 = \dfrac {136} 4 = 34$

$\blacksquare$