Madular multiplicative inverse

The modular multiplicative inverse of an integer a modulo n is an integer b so that $ab \equiv 1 \pmod{n}$ . If a is its own inverse, then $a^2 \equiv 1 \pmod{n}$ .

For this to be true for all a coprime to and less than n, $\lambda(n) = 2$ , where $\lambda$ is the Carmichael function. $\boxed{24}$ is the maximum n for which $\lambda(n) = 2$ is satisfied.