Each book has an unique International Standard Book Number (ISBN-10), a 10 - digit code x1, x2, dots,x10 assigned by the publisher that identifies the language, the publisher, the number assigned to the book by its publishing company, and finally a check digit which is either a digit or the letter x to represent 10 . This check digit is defined by x10 - = ∑⁹ᵢ₌₀ x(mo11) . Prove that ∑¹⁰ᵢ₌₀ x - = 0(mo11)