Lehmer's totient problem

In mathematics, Lehmer's totient problem asks whether there is any composite number n such that Euler's totient function φ(n) divides n − 1. This is an unsolved problem.

For Lehmer's Mahler measure problem, see Lehmer's conjecture.
Unsolved problem in mathematics:

Can the totient function of a composite number divide ?

(more unsolved problems in mathematics)

It is known that φ(n) = n − 1 if and only if n is prime. So for every prime number n, we have φ(n) = n − 1 and thus in particular φ(n) divides n − 1. D. H. Lehmer conjectured in 1932 that there are no composite numbers with this property.

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