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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A residue number system (RNS) represents a large integer using a set of smaller integers, so that computation may be performed more efficiently. It relies on the Chinese remainder theorem of modular arithmetic for its operation, a mathematical idea from Sun Tsu Suan-Ching (Master Sun''s Arithmetic Manual) in the 4th century AD.