# For How Large an 'n' can the Carmichael Function of n be 2?

1. Jun 4, 2015

### patrickbotros

What is the largest n such that λ(n)=2? Is there such a bound? This isn't a homework question. I'm just interested.

2. Jun 5, 2015

### certainly

If $p$ is not in $n$ than $(p,n)=1$.
Therefore for $p^2\equiv 1mod(n)$ to hold $n=6a$ since all $p$ other than 2 and 3 are of the form $6b\pm 1$
Also all $p\leq \sqrt{n}$ must be in $n$ since otherwise $p^2<n$.
so we need a $p\sharp$ such that $p_{c+1}>\sqrt{p\sharp}$.
It's easy to see that this does not hold for $p>5$.
[EDIT:-$p\sharp=p_1\times p_2 \times p_3\times.......\times p_c$.]