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Many aspects of modern society rely upon unique numbers to verify the authenticity of certain objects. Bank notes utilize serial numbers, cars and trucks use vehicle identification numbers, books are given International Standard Book Numbers (ISBNs), and many consumer products have bar codes or other identification numbers. Fortunately, a simple system involving numbers called check digits can verify the authenticity of all sorts of serial and registration numbers. Discover the many check-digit systems, and delve into some fascinating mathematics concerning modular arithmetic, symmetries, and group theory.