Published 2025-08-08
DOI:
https://doi.org/10.71712/Keywords
- quadratic polynomials
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
Kozhushkina, O., Hallare, M. B., Jane Long, Moll, V. H., Pedjeu, J.-C., Thompson, B., & Trulen, J. (2025). The valuation tree for \(\ n^2 + 7\). Scientia Series A: Mathematical Sciences, 30, 91-102. https://doi.org/10.71712/
Abstract
The 2-adic valuation of an integer \( x\) is the highest power of 2 which divides \( x\) It is denoted by \(\ v_2(x).\) The goal of the present work is to describe the sequence \(\{v_2(n^2 + a)\}\) for \(\ 1 \leq a \leq 7\)\) The first six cases are elementary. The last
case considered here, namely \(\ a = 7\), presents distinct challenges. It is shown here how to represent this family of valuations in the form of an infinite binary tree, with two symmetric infinite branches.
