Ford's Theorem
Ford (1999) proved that for every integer k ≥ 2 there is a number m for which the equation φ(x) = m has exactly k solutions; this result had previously been conjectured by Wacław Sierpiński. However, no such m is known for k = 1. Carmichael's totient function conjecture is the statement that there is no such m.
Read more about this topic: Euler's Totient Function
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