09/11/2014, 08:48 AM

Considering collatz and the idea of a nontrivial cycle of odd length L , I have this lemma :

If a nontrivial collatz cycle of odd lenght L exists , one of its values must be representable by

a mod p

for some 0 =< a < p with p a prime ,

division by 2 is then given by multiplication by (1/2) mod p.

multiplication by 3 is still the same ( reduced mod p ).

And p is an odd prime divisor of L.

regards

tommy1729

If a nontrivial collatz cycle of odd lenght L exists , one of its values must be representable by

a mod p

for some 0 =< a < p with p a prime ,

division by 2 is then given by multiplication by (1/2) mod p.

multiplication by 3 is still the same ( reduced mod p ).

And p is an odd prime divisor of L.

regards

tommy1729