{"id":"hexagon/2611.00097","pdf":"https://hexagonmath.org/pdf/2611.00097v1","url":"https://hexagonmath.org/abs/2611.00097v1","tags":["msc:11A63","msc:11A07","msc:11B50","msc:11N13","msc:11N69","congruence speed","eventual periodicity","integer tetration","lifting-the-exponent lemma","natural density"],"score":0,"title":"Nonconstant Congruence Speeds of Integer Tetration in Non-Squarefree Radices","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Marco Ripà"],"reviews":0,"subject":"math.NT","summary":"We further develop the theory of congruence speed for integer tetration in non-squarefree numeral systems, building on Appendix B of [M. Ripà and G. Di Pietro (2026), A compact notation for peculiar properties characterizing integer tetration, Notes on Number Theory and Discrete Mathematics, 32(3), 477–496]. For bases coprime to the radix, we establish an eventual floor-difference representation and determine the exact spectrum of attainable least periods. We construct explicit arithmetic progressions containing infinitely many prime bases with nonconstant congruence speed for every…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}