homework and exercises - Proof that 4-potential exists from Gauss-Faraday field equation

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 $$F_{\alpha \beta}~=~\partial_{\alpha} A_{\beta} - \partial_{\beta} A_{\alpha}~?$$