Abstract
An elementary proof by contradiction of the Collatz Conjecture (CC) (also known as the '3X + 1' Conjecture), is presented. A modified form of the Collatz transformation is formulated, leading to the concept of a modified Collatz chain. A smallest counterexample N0 is hypothesized; the existence of N0 implies that N0 must generate an infinite sequence {Nk}, each of whose elements is at least as large as N0. A formula for Nk is derived, in terms of an auxiliary sequence {Ek} and the starting value N0. It is shown that each Ek satisfies k = Ek < 1.585k; this, in turn, leads us to conclude that N0 is unbounded, which is a contradiction of its definition, thereby establishing CC.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematical Education in Science and Technology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
