TY  - UNPB
TI  - Orbits Theory. A Complete Proof of the Collatz Conjecture
ID  - uneatlantico614
A1  - Crespo Álvarez, Jorge
AV  - public
Y1  - 2021/12//
JF  - Cambridge Open Engage
N2  - In this work a complete proof of the Collatz Conjecture is presented. The solution assumes as hypothesis that Collatz's Conjecture is a consequence. We found that every natural number n_i?N can be calculated starting from 1, using the function n_i=((2^(i-?)-C))?3^? , where: i?0 represents the number of steps (operations of multiplications by two subtractions of one and divisions by three) needed to get from 1 to n_i, ??0 represents the number of multiplications by three required and 0?C?2^(i-?i/3? )-2^((i mod 3)) 3^?i/3? is an accumulative constant that takes into account the order in which the operations of multiplication and division have been performed. Reversing the inversion, we have obtained the function: ((3^? n_i+C))?2^(i-?)=1 that proves that Collatz Conjecture it?s a consequence of the above and also proofs that Collatz Conjecture it?s true since ((3^? n_i+C))?2^(i-?) is the recursive form of the Collatz?s function.
UR  - http://doi.org/10.33774/coe-2021-9w3gs
ER  -