Necessary and sufficient conditions are established for zero-sum Γ-magic squares of order n on Abelian groups Γ of order n².
Skolem, On certain distributions of integers in pairs with given differ- ences,Mathematica Scandinavica5(1957), 57–68
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Note on zero-sum magic squares on Abelian groups
Necessary and sufficient conditions are established for zero-sum Γ-magic squares of order n on Abelian groups Γ of order n².