{"id":"hexagon/2610.00234","pdf":"https://hexagonmath.org/pdf/2610.00234v1","url":"https://hexagonmath.org/abs/2610.00234v1","tags":["msc:11J71","uniform distribution"],"score":0,"title":"An unavoidable set of divisors for the nearest integers to ξ(3/2)^n","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Ralf Stephan"],"reviews":0,"subject":"math.NT","summary":"We prove that for every real ξ ̸= 0 the sequence of nearest integers [ξ(3/2)^n + 1/2], n ∈ N, contains infinitely many elements divisible by 2 or by 5. In particular, for ξ > 0 infinitely many of these nearest integers are composite. This is the nearest-integer counterpart of the theorem of Forman and Shapiro on [ξ(3/2)^n], for which Dubickas and Novikas give the unavoidable set {2, 5, 7, 11}; for nearest integers two primes suffice. The proof follows the method of Dubickas and Novikas: if 2 and 5 divide only finitely many terms, the sequence of operations is forced to become (A^2B^2)^∞,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-10-14","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}