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[Collatz] Tommy's collatz lemma - Printable Version

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[Collatz] Tommy's collatz lemma - tommy1729 - 09/11/2014

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.