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The problem was originally posed by Molnar in [molnar1974matrix].

Various authors followed up this article with both single solutions and parametric families of solutions:

• American Mathematical Monthly, 82, pages 999-1000, 1975.
• American Mathematical Monthly, 84, page 809, 1977.
• American Mathematical Monthly, 94, page 962, 1987.

Guy presents an overview and discusses variants of the problem [guy2004unsolved].

A CSP model is presented in [frisch2003constraints]

[guy2004unsolved]
Richard Guy
Unsolved problems in number theory
Springer
2004

[frisch2003constraints]
Alan M Frisch, Chris Jefferson, and Ian Miguel
Constraints for breaking more row and column symmetries
Principles and Practice of Constraint Programming–CP 2003, 2003

[molnar1974matrix]
EA Molnar
A matrix problem
American Mathematical Monthly, 1974