In this paper, we propose an error detection scheme of phase offsets for binary sequences including PN (Pseudo Noise) sequences based on the number theoretical approach. It is important to know phase offsets of spreading sequences in the CDMA (Code Division Multiple Access) mobile communication systems because phase offsets of the same spreading sequence are used to achieve the acquisition and are used to distinguish each base station. When the period of the sequence is not very long, the relative phase offset between the sequence and its shifted replica can be found by comparing them, but as the period of the sequence increases it becomes difficult to find the phase offset. The error detection failure probability of the proposed method is derived, and it is confirmed by the simulation results. We also discuss the circuit realization of the proposed method and show it can be easily implemented.