Lehmer's totient problem
Unsolved problem in mathematics / From Wikipedia, the free encyclopedia
For Lehmer's Mahler measure problem, see Lehmer's conjecture.
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.
Unsolved problem in mathematics:
Can the totient function of a composite number divide ?
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]