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Minimum values of the Carmichael function

Problem 533 Published on Sunday, 8th November 2015, 10:00 am; Solved by 243;
Difficulty rating: 50%

The Carmichael function λ(n) is defined as the smallest positive integer m such that am = 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.