**Examples**

The totient function φ(*n*) is equal to 2 when *n* is one of the three values 3, 4, and 6. Thus, if we take any one of these three values as *n*, then either of the other two values can be used as the *m* for which φ(*m*) = φ(*n*).

Similarly, the totient is equal to 4 when *n* is one of the four values 5, 8, 10, and 12, and it is equal to 6 when *n* is one of the four values 7, 9, 14, and 18. In each case, there is more than one value of *n* having the same value of φ(*n*).

The conjecture states that this phenomenon of repeated values holds for every *n*.

Read more about this topic: Carmichael's Totient Function Conjecture

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