# This appears to be in direct violation of Carmichael's theorem.

by Whovian
Tags: appears, carmichael, theorem, violation
According to Wikipedia, for ##n\geq4## $$\lambda(10^n)=\text{lcm}\left(\lambda(2^n), \lambda(5^n)\right)=\text{lcm}\left(\frac{1}{2}\varphi(2^n), \varphi(5^n)\right)=\ldots=5\cdot10^{n-2},$$ and everything is right with the universe?