Some properties of magSome Properties of Magic Squares of Distinct Squares and Cubesic squares

amal Abdulrahman Ibrahim, Shatha A. Salman


Magic squares is n×n matrix with positive integer entries as well as the sum of rows, columns
and mains diagonal have the same magic constant, one of the most oldest magic square was
discovered in china. In this paper the history of magic square is displayed and some definition
of its kind is given the prove of two theorems about properties of magic square is introduced.

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Ahmed M.M., Algebraic combinatorics of magic squares, PhD thesis, University of California, 2004.

Beck M., Robins S., Computing the continuous discretely, Springer Science+ Business Media, LLC, 2007.

Boyer, C., Some notes on the magic squares of squares problem, The Mathematical Intelligencer, 27, 2, 2005, pp.52-64.


Cammann S., Old Chinese magic squares, Verlag für Recht und Gesellschaft, 1962.

Heath-Brown D.R., Lioen W.M., Te Riele H.J.J., On solving the Diophantine equation ³+ ³+ ³= on a vector computer, Mathematics of computation, 61,203, 235-244, 1993.


Koyama K., Tsuruoka Y., Sekigawa H., Tables of solutions of the Diophantine equation ³+ ³+ ³In n, Math, Comput, 1994.

Koyama K., Tsuruoka Y., Sekigawa H., On searching for solutions of the Diophantine equation ³+ ³+ ³= , Mathematics of Computation of the American Mathematical Society, 66,218, 841-851, 1997.

Mahler K., Note on hypothesis K of Hardy and Littlewood, Journal of the London Mathematical Society, 1,2, 136-138, 1936.

Mordell L.J., On sums of three cubes, Journal of the London Mathematical Society, 1, 3, 139-144, 1942.

Miller J.C.P., Woollett M.F.C., Solutions of the Diophantine Equation: x3+ y3+ z3= k, Journal of the London Mathematical Society, 1, 1, 101-110, 1955.

Nathanson M.B., Additive Number Theory the Classical Bases, Springer Science & Business Media, 164, 2013.

Nowlan R.A., Magic Squares and Art, In Masters of Mathematics. SensePublishers, Rotterdam. 545-566, 2017.


Pickover C.A., Pickover, S.S.C.A., the Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures Across Dimensions, Princeton University Press, 2002.

Rabern L.W., Properties of magic squares of squares, Rose-Hulman Undergraduate Mathematics Journal, 4, 1, 3, 2003.

Robertson J.P., Magic squares of squares, Mathematics Magazine, 69, 4, 289-293, 1996.

Ryley S., The Ladies' Diary, 122, 35, 1825.

Schuyler C., Islamic and Indian magic squares, Parts I and II. History of Religions 8, 181-209, 271-299, 1969.


Swetz F., Legacy of the Luoshu: The 4,000 Year Search for the Meaning of the Magic Square of Order Three, AK Peters/CRC Press, 2008.

Shafarevich, I.R. and Remizov, A.O., Linear algebra and geometry, Springer Science & Business Media, 2012.

[Crossref], [PubMed]



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