Generalizing Lehmer’s totient problem
Marius Tărnăuceanu
University “Al. I. Cuza”, Iasi, Romania
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Abstract
An important unsolved question in number theory is Lehmer's totient problem that asks whether there exists any composite number such that , where is the Euler's totient function. It is known that if any such exists, it must be odd, square-free, greater that , and divisible by at least distinct primes. Such a number must be also a Carmichael number.
In this short note, we discuss a group-theoretical analogous problem involving the function that counts the number of automorphisms of a finite group. Another way to generalize Lehmer's totient problem is also proposed.
Cite this article
Marius Tărnăuceanu, Generalizing Lehmer’s totient problem. Elem. Math. 79 (2024), no. 2, pp. 77–79
DOI 10.4171/EM/492