#### Title

The valuation tree for n2+7

#### Document Type

Article

#### Publication Date

2020

#### Publication Title

SCIENTIA Series A: Mathematical Sciences

#### Abstract

The 2-adic valuation of an integer x is the highest power of 2 which

divides x. It is denoted by ν2(x). The goal of the present work is to describe the

sequence {ν2(n2+ a)}for 1 6a 67. 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.

#### Volume

30

#### First Page

91

#### Last Page

102

#### ISSN

0716-8446

#### Repository Citation

Kozhushkina, O.; Hallare, M. B.; Long, J.; Moll, V.; Pedjeu, J.-C.; Thompson, B.; Trulen, J.; The valuation tree for n2+7, Scientia, Series A, Volume 30 (2020), 91-102. Available at http://scientia.mat.utfsm.cl/vol30.html