All magic squares as sums of two magic squares
Abstract
Several new methods of construction of magic squares of different orders including order of 2N when N is even or odd have been presented along with underlying proofs. The methods have been shaped in form of algorithm that are very convenient for writing programs for construction of magic squares of any order. A method of obtaining two very convenient orthogonal latin squares of any odd order has been given and these have been used to construct magic squares of any odd order. A method of obtaining magic squares of order N = pq by using magic squares of orders p and q has been given. The methods have been illustrated by constructing magic squares of orders 3, 4, 6, 12 and 14. Using magic squares of order 4 and odd primes any magic squares can be obtained by using these methods based on summation of two magic squares.
