English

2-adic Valuations of Quadratic Sequences

Number Theory 2021-09-01 v4

Abstract

Properties of 2-adic valuation sequences for general quadratic polynomials with integer coefficients are determined directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at terminating nodes. We completely describe the periodic sequences in the bounded case. Throughout, we frame results in terms of trees and sequences.

Keywords

Cite

@article{arxiv.2012.10332,
  title  = {2-adic Valuations of Quadratic Sequences},
  author = {Will Boultinghouse and Jane Long and Olena Kozhushkina and Justin Trulen},
  journal= {arXiv preprint arXiv:2012.10332},
  year   = {2021}
}

Comments

26 pages, 4 figures. Updated proofs and conditions on some theorems. Made background information clearer. Add two more examples and four tables

R2 v1 2026-06-23T21:04:51.632Z