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Moreover, the numbers of solutions of the depressed cubic equation in domains $\\bz_p^{*},\\bz_p,\\bq_p$ are provided. Since $\\bbf_p\\subset\\bq_p,$ we generalize J.-P. Serre's \\cite{JPSJ} and Z.H.Sun's \\cite{ZHS1,ZHS3} results concerning with depressed cubic equations over the finite field $\\bbf_p$. 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