English

A note on multiplicative-inverse chaining in finite fields

Number Theory 2025-07-31 v1 Combinatorics

Abstract

We consider chaining multiplicative-inverse operations in finite fields under alternating polynomial bases. When using two distinct polynomial bases to alternate the inverse operation we obtain a partition of FpnFp\mathbb F_{p^n}\setminus \mathbb F_p into disjoint cycles of even length. This allows a natural interpretation of the cycles as permutation cycles. Finally, we explore chaining under more than two polynomial bases.

Keywords

Cite

@article{arxiv.2507.22142,
  title  = {A note on multiplicative-inverse chaining in finite fields},
  author = {Divyarthi Mohan and R. Ravindraraj},
  journal= {arXiv preprint arXiv:2507.22142},
  year   = {2025}
}
R2 v1 2026-07-01T04:24:43.678Z