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Sign detection in Non-Redundant Residue Number System with reduced information

A necessary and sufficient condition for sign detection in Non-Redundant Residue Number System by reducing the information of a residue digit has been obtained. The function to reduce the information of a residue digit xp corresponding to a modulus mp has been assumed to be periodic with the period length equation, where equation and equation. A sequential method for determining the sign of a number is shown to demonstrate the applicability of the results thus proved.