This is a problem concerning covariant formulation of electromagnetism.
Given $$\partial_{[\alpha} F_{\beta\gamma]}~=~ 0 $$ how does one prove that $F$ can be obtained from a 4-potential $A$ such that $$F_{\alpha \beta}~=~\partial_{\alpha} A_{\beta} - \partial_{\beta} A_{\alpha}~? $$
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