Carmichael function: Difference between revisions

Revision as of 15:11, 7 January 2022

Revision as of 23:10, 12 January 2022

Line 123:

:<math> a\,|\,b \Rightarrow \lambda(a)\,|\,\lambda(b) </math>

'''Proof.''' The result follows from the formulaChinese remainder theorem.

By definition, for any integer <math>k</math>, we have that <math> k^\lambda(b) \equiv 1\mod{b} </math> , and therefore <math>k^{\lambda(b)} \equiv 1\mod{a}</math>.

:<math>\lambda(n) = \operatorname{lcm}\left(\lambda\left(p_1^{r_1}\right),\lambda\left(p_2^{r_2}\right),\ldots,\lambda\left(p_k^{r_k}\right) \right)</math>

By the minimality property above, we have <math> \lambda(a)\,|\,\lambda(b) </math>.

mentioned above.

===Composition===