(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/nat/totient".
-
include "nat/chinese_reminder.ma".
include "nat/iteration2.ma".
definition totient : nat \to nat \def
\lambda n.sigma_p n (\lambda m. eqb (gcd m n) (S O)) (\lambda m.S O).
-
+lemma totient1: totient (S(S(S(S(S(S O)))))) = ?.
+[|simplify.
+
theorem totient_times: \forall n,m:nat. (gcd m n) = (S O) \to
totient (n*m) = (totient n)*(totient m).
intros.