Considerations on the Collatz Conjecture

Abstract

Audemir Loris

Part of the scientific community has spent considerable time and resources to somehow validate Collatz’s conjecture, countless efforts have achieved considerable progress in this direction, but this conjecture lacked definitive confirmation that choosing an odd number any xi ∈ N∗ , we will obtain x(i+1) = 3xi + 1, this being an even number x(i+1), divide it if the same by the number two (successively) until another odd number ∈ N∗ is obtained, the process xn = 3x(n−1) + 1 and divisions by two until the result is a number equal to 1. This work presents deductions, algorithms and equations that corroborate this proposition, supporting this perception and conclusion that Collatz’s conjecture points to the final cycle 4 → 2 → 1.

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