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For an increased level of scalability, availability and durability, some customers may want their data to be replicated on multiple cloud servers. The more copies the cloud service provider (CSP) is asked to store, the more fees the customers are charged. In this paper, we propose a pairing-based provable multi-copy data possession (PB-PMDP) scheme, which provides an evidence to the customers that all outsourced copies are actually stored and remain intact. Moreover, it allows authorized users (i.e., those who have the right to access the owner's file) to seamlessly access the file copies stored by the CSP, and supports public verifiability. The proposed scheme is proved to be secure against colluding servers. We illustrate the performance of the PB-PMDP scheme through theoretical analysis, which is validated by experimental results. The verification time of our scheme is practically independent of the number of file copies. Additionally, we discuss how to identify corrupted copies by slightly modifying the proposed PB-PMDP scheme.