Airline Ticket Identification Numbers

Airline tickets have 15-digit identification numbers associated with them. The first 14 digits identify the ticket and the 15th (the last one) is the check digit. 

Definition 23 1. Let oi-020304 OsaeaTa Uoaioanaijaisau be the 14-number associated with an airline ticket The check digit 015, which is appended to this number to create the identification monber 01-020304-05060708090100110x2013014-015. is determined by ... 

Suppose that the following two numbers are airline ticket identification numbers. Using the airline ticket check digit scheme, determine which is a valid number and... 

Since airline ticket numbers are large, the exercise will be completed with much smaller four-digit numbers, ai 020304. The scheme works in the same manner. The check digit 04 is appended to the three-digit number 010303 to create the identification number 01030304 such that 04 satisfies the equation 04 = 010303 (mod 7). These numbers are easier to work with, but the mathematical concept is the same. 

Identification numbers, and the check digit schemes that detect when these numbers have been transmitted inconectly, are crucial for the quick storage, retrieval, and transfer of vast amounts of information. In this book, a variety of check digit schemes are discussed. Gieck digit schemes vary in their ability to catch errors. Some, such as the airline ticket scheme, do not catch every occurrence of the most connnon type of error, while others, such as the ISBN scheme, catch most error patterns. Consequently, criteria for judging the reliability of check digit schemes are a central concern of this book. 

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