Work

The valuation tree for \(\ n^2 + 7\)

Year: 2025

Type: article

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.

Source: Scientia Series A: Mathematical Sciences

DOI: 10.71712/adsc-sw47

Authors: Kozhushkina, Olena, Hallare, Maila Brucal, Long, Jane, Moll, Victor H., Pedjeu, Jean-Claude, Bianca

Institutions: Ursinus College, Norfolk State University, Stephen F. Austin State University, Tulane University, Tennessee State University, Westminster University, University of Westminster

Language: English

Topic: advanced mathematical theories

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7080798157

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