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In this paper we solve analytically the problem of distributing optimally a set of t slots between a group of n readers in RFID dense environments where a single frequency channel is available. In these environments, the readers within reader-to-reader interference range must transmit at different times, otherwise tags cannot identified. This resource allocation problem is addressed for both static and dynamic Frame Slotted Aloha, which are the most broadly extended mechanism used in UHF RFID systems. The goal is maximizing the expected number of tags successfully identified within the t slots. Results demonstrate that the optimal solution outperforms an assignment proportional to the number of tags in each reader. The results heavily depend on the underlying reading algorithm of the reader.