An Extension of Waring's Problem in $\mathbb{Z}_{p^k}$

An-Ping Li

An Extension of Waring's Problem in $\mathbb{Z}_{p^k}$

Combinatorics 2019-05-01 v9 Number Theory

Authors: An-Ping Li

Abstract

In this paper, we will investigate the solvability of the equation $x_1^k + x_2^k + \ldots + x_s^k = n$ , $n\in \mathbb{Z}_{p^k}$ , $x_1,...,x_s\in \mathcal{A}$ , $\mathcal{A}\subseteq \mathbb{Z}_{p^k}$ . We will give a upper bound of the number of solutions for $s=2$ .

Keywords

waring's problem modular arithmetic zeta_{p^k} solvability upper bound number of solutions

Cite

@article{arxiv.1808.04532,
  title  = {An Extension of Waring's Problem in $\mathbb{Z}_{p^k}$},
  author = {An-Ping Li},
  journal= {arXiv preprint arXiv:1808.04532},
  year   = {2019}
}

Comments

We feel that the proofs of two main Lemmas 2.7 and 4.7 seems not impeccable, and unconvincing more or less

An Extension of Waring's Problem in $\mathbb{Z}_{p^k}$

Abstract

Keywords

Cite

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