## Minimum values of the Carmichael function

### Problem 533

The **Carmichael function** λ(`n`) is defined as the smallest positive integer `m` such that `a ^{m}` = 1 modulo

`n`for all integers

`a`coprime with

`n`.

For example λ(8) = 2 and λ(240) = 4.

Define L(`n`) as the smallest positive integer `m` such that λ(`k`) ≥ `n` for all `k` ≥ `m`.

For example, L(6) = 241 and L(100) = 20 174 525 281.

Find L(20 000 000). Give the last 9 digits of your answer.