A Short Elementary Proof of the Unprovability of the Collatz Conjecture
Journal of Advances in Mathematics and Computer Science · pp. 3023–3027 · Published 19 Aug 2014
10.9734/BJMCS/2014/12538Abstract
Consider any positive integer n. If n is even, halve it. If n is odd, multiply it by 3 and add 1. This algorithm is then repeated indefinitely. It has been conjectured by Collatz that this process, which is also known as Hasse’s algorithm, eventually reaches 1. A new perspective on this problem is offered by considering Hasse’s algorithm in binary representation. Some important consequences are used to establish that no proof of the Collatz conjecture exists.
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