Lehmer's totient problem

Unsolved problem in mathematics:

Can the totient function of a composite number ${\displaystyle n}$ divide ${\displaystyle n-1}$?

(more unsolved problems in mathematics)

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.

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.^[1]