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- W3174510051 abstract "Lehmer's totient problem asks whether there exists any composite number $n$ such that $varphi(n) , mid , (n-1)$, where $varphi$ is Euler totient function. It is known that if any such $n$ exists, it must be Carmichael and $n > 10^{30}$. In this paper, we develop a new approach to the problem via some recent results in group theory related to a function $psi$ (the sum of order of elements of a group) and show that if $k varphi(n) = n-1$ for some integer $k$, then $k$ must be $geq 3$, and actually, if $5, 7, 11, 13 not | n$, $k geq 4$. This implies that any counterexample must be such that $n > 10^{8171}$ and $omega(n) geq 1991$." @default.
- W3174510051 created "2021-07-05" @default.
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- W3174510051 date "2021-06-21" @default.
- W3174510051 modified "2023-09-27" @default.
- W3174510051 title "A group-theoretical approach to Lehmer's totient problem" @default.
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