Polynomials whose nth powers have prescribed multiple-of-nth-degree coefficients

Jeffrey Yelton

Polynomials whose nth powers have prescribed multiple-of-nth-degree coefficients

Number Theory 2025-06-02 v1 Algebraic Geometry

Authors: Jeffrey Yelton

Abstract

We show under a mild hypothesis that given field elements $a_0, \dots, a_m \in K$ , there always exists a degree- $m$ polynomial whose $n$ th power whose degree- $jn$ coefficient is equal to $a_j$ for $0 \leq j \leq m$ . We provide an alternate proof for the $n = 2$ case which is more constructive.

Keywords

generative AI critical thinking metacognitive prompts search behavior human-AI interaction

Cite

@article{arxiv.2505.24013,
  title  = {Polynomials whose nth powers have prescribed multiple-of-nth-degree coefficients},
  author = {Jeffrey Yelton},
  journal= {arXiv preprint arXiv:2505.24013},
  year   = {2025}
}

Comments

4 pages, 0 figures, requires knowledge of some basic notions in algebra and algebraic geometry but intended to be very accessible

Polynomials whose nth powers have prescribed multiple-of-nth-degree coefficients

Abstract

Keywords

Cite

Comments

Related papers