The International Standard Book Number (ISBN) for a given book is a unique number allowing publishers and vendors to distinguish between publications, even those with the same title and/or author. The first twelve digits of an ISBN value are used to identify the region, publisher, and title of the book, while the final digit is a check digit. This means that its value is chosen based on a mathematical combination of all the other digits in the ISBN - this makes it easy to recognize when someone has mistyped one of the digits in the ISBN, because the mathematical expression used on the digits won't result in the correct value. In particular, for modern ISBN-13 numbers, the formula is as follows: (x+3x2+x3+3X4+X5+3Xs+X7+3Xg+Xg+3x10+X11+3X12+X13) % 10 = 0 Where x represents the first digit, x2 represents the second digit, and so on. For example, the ISBN-13 of the paperback version of The Martian is 9780553418026. If you plug the digits into the formula, the result is 0: (9+3*7+8+30+5+3 5+3+3*4+1+3*8+0+3*2+6) % 10 (9+21+8+0+5+15+3+12+1+24+0+ 6 + 6 ) % 10 (110) % 10 0