A Dual-Radix Approach to Steiner's 1-Cycle Theorem

Abstract

This article presents a variety of algebraic proofs of Steiner's $1$-Cycle Theorem. It also demonstrates that, under an exponential upper-bound on the iterates, the only $1$-cycles in the (accelerated) $3x-1$ dynamical system are $(1)$ and $(5,7)$.

Minor edits; 16 pages; to appear in the proceedings of the "Combinatorial and Additive Number Theory (CANT) 2018" conference