Year: 2026
Type: preprint
Abstract: We study three innocent-looking recurrences modulo $3$, each built from squares of two earlier terms. One of them turns out to be secretly $\textit{linear}$, and we can compute its periods exactly. One is a $\textit{permutation}$ hiding a small, perfectly orderly piece inside a large, random-looking one. The third looks thoroughly random, but it still has a few provable features. Along the way we meet open problems that need nothing beyond a first course in abstract algebra to state. This paper is a starting point, not the final word in any sense.
Source: arXiv (Cornell University)
Author: Finch, Steven
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223791644