# Nick Harland

## The Iterated Carmichael Lambda Function

Date Friday, October 12, 2012

The Carmichael lambda function is defined to be the smallest exponent $m$ such that $a^m$ is congruent to 1 modulo $n$ for all $a$ coprime to $n.$ This classical function is strongly related to the Euler totient function. We will discuss some interesting problems related to this function. We will also discuss some analytic properties of the iterated Carmichael lambda function, defined to be the Carmichael function composed with itself $k$ times.