@unpublished{uneatlantico614,
       booktitle = {Orbits Theory. A Complete Proof of the Collatz Conjecture},
           title = {Orbits Theory. A Complete Proof of the Collatz Conjecture},
          author = {Jorge Crespo {\'A}lvarez},
         journal = {Cambridge Open Engage},
            year = {2021},
           month = {Diciembre},
        abstract = {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{$\leq$}C{$\leq$}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.},
             url = {http://repositorio.uneatlantico.es/id/eprint/614/}
}