Magic Square: An nxn square where every horizontal,vertical, and diagonal line all add up to the same number.
Magic Constant: The number which every line with a magic square adds up to
So most magic squares, have a magic constant. But some do not. A fairly trivial answer is 0x0. Where no numbers are present, therefore it cannot sum up into any number.
A less than trivial answer but not complicated answer is 2x2. No possible configuration of 1,2,3,4 within a 2x2 block can have all lines add up to the same number. If it were possible it would theoretically be 5
So besides 0, and 2 are there any other positive dimensions for a magic square that do not have a magic constant? Technically making all possible configurations invalid magic squares?
Mathematical Proof is Appreciated!