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In this paper, we propose a novel application of residue number system (RNS) arithmetic in designing hopping-pilot patterns for cellular downlink orthogonal frequency-division multiple access (OFDMA). By hopping the scan lines in either the time or the frequency domain, RNS-based pilot patterns fulfill the Nyquist sampling theorem. That is, by using RNS-based pilot patterns, the channel's delay-Doppler response can fully be reconstructed without severe aliasing. In addition to channel estimation, our proposed scheme can achieve other objectives, such as device/cell identification and time-frequency synchronization. We show that the RNS-based approach has more pairs of hopping-pilot patterns that are collision free than the Costas-array-based method. This is helpful in not only mitigating intra-/intercell interference but also identifying multiple devices in a multicell multiantenna environment. Moreover, hopping in time increases the pilot's time support, which, in turn, enables quick initial acquisition of time-frequency offsets.