Document Type : Research Articles


Department of Mathematics, Babol Branch, Islamic Azad University, Babol, Iran



Over eighty years ago, the German mathematician Lothar Collatz formulated an
interesting mathematical problem, which he was afraid to publish, for the
simple reason that he could not solve it. The Collatz conjecture is an
elusive problem in mathematics regarding the oneness of natural numbers when
running through a specific function based on being odd or even, specifically
stating that regardless of the initial number the series will eventually
reach the number $1$. In this paper, an elementary proof of the Collatz
conjecture is presented and generalized.