Lehmer's totient problem

For Lehmer's Mahler measure problem, see Lehmer's conjecture.
Unsolved problem in mathematics:
Can the totient function of a composite number n divide n 1?
(more unsolved problems in mathematics)

In mathematics, Lehmer's totient problem, named for D. H. Lehmer, asks whether there is any composite number n such that Euler's totient function φ(n) divides n  1. This is true of every prime number, and Lehmer conjectured in 1932 that there are no composite solutions: he showed that if any such n exists, it must be odd, square-free, and divisible by at least seven primes (i.e. ω(n) ≥ 7). Such a number must also be a Carmichael number.

Properties

References

  1. Sándor et al (2006) p.23
  2. Guy (2004) p.142
  3. Sándor et al (2006) p.24

External links

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