Abstract
A composite positive integer [Formula: see text] has the Lehmer property if [Formula: see text] divides [Formula: see text] where [Formula: see text] is an Euler totient function. In this paper, we shall prove that if [Formula: see text] has the Lehmer property, then [Formula: see text], where [Formula: see text] is the number of prime divisors of [Formula: see text]. We apply this bound to repunit numbers and prove that there are at most finitely many numbers with the Lehmer property in the set [Formula: see text] where [Formula: see text] denotes the highest power of 2 that divides [Formula: see text], and [Formula: see text] is a fixed real number.
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