Problem 533
Minimum values of the Carmichael function
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.
卡迈克尔函数的最小值
卡迈克尔函数 λ(n)被定义为使得所有与n互质的整数a都满足在同余意义下am = 1的最小正整数m。
例如，λ(8) = 2，而λ(240) = 4。
记L(n)是最小的满足下列条件的正整数m：对于所有k ≥ m都有λ(k) ≥ n。
例如，L(6) = 241，而L(100) = 20 174 525 281。
求L(20 000 000)。给出其最后9位数字作为你的答案。