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In this letter, we investigate joint radio resource allocation and edge offloading decision optimization in a multi-cell orthogonal frequency-division multiple access cellular network in order to minimize system's energy consumption. The discrete subchannel allocation and offloading decision variables as well as the interference incorporated in the data rate function make the stated optimization problem a mixed integer non-linear programming. To address this problem and obtain a locally optimal solution, we use the variable relaxation and majorization minimization method. Via simulation results, we demonstrate that our proposed solution results in a considerable reduction of system's power consumption.