UNSOLVED PROBLEMS

In Number Theory, Logic, and Cryptography

Semi-Magic Square of Cubes

 

A square is semi-magic if all of the rows and columns add up to the same total.  So, for example, the square

 

 

 

 

is semi-magic, since every row and column adds up to 25.  The following semi-magic square is interesting because eight of the nine entries are perfect cubes:

 

 

 

 

The problem is to find a 3 by 3 semi-magic square all of whose entries are distinct positive integer cubes, or prove that such a square cannot exist.

 

For further information, please see:

[1] http://www.multimagie.com/indexengl.htm

[2] http://home.earthlink.net/~morgenstern/magic/cb3.htm

[3] https://books.google.com.au/books?id=-mu8O8RMG6QC

 

 

You can check for contributions to this problem on the solutions page.

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