Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In number theory, the totient varphi(n) of a positive integer n is defined to be the number of positive integers less than or equal to n that are coprime to n (i.e. having no common positive factors other than 1). In particular varphi(1)=1 since 1 is coprime to itself (1 being the only natural number with this property). For example, varphi(9)=6 since the six numbers 1, 2, 4, 5, 7 and 8 are coprime to 9. The function varphi so defined is the totient function.

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