Explicit Algebraic Numbers all whose Integer Parts of Powers are Composite

Suyeong Hahn; Dan Ismailescu; Ganghun Kim; Minseung Kim

Explicit Algebraic Numbers all whose Integer Parts of Powers are Composite

Number Theory 2026-08-05 v1

Authors: Suyeong Hahn , Dan Ismailescu , Ganghun Kim , Minseung Kim

Abstract

We present several explicit classes of algebraic integers $\alpha>1$ such that $\lfloor \alpha^n\rfloor$ is composite for all but finitely many $n$ .

Cite

@article{arxiv.2608.05309,
  title  = {Explicit Algebraic Numbers all whose Integer Parts of Powers are Composite},
  author = {Suyeong Hahn and Dan Ismailescu and Ganghun Kim and Minseung Kim},
  journal= {arXiv preprint arXiv:2608.05309},
  year   = {2026}
}