The valuation tree for n2+7

Olena Kozhushkina; Maila Bruca Hallare; Jane H. Long; Victor H. Moll; Jean-Claud Pedjeu; Bianca Thompson; Justin Trulen

The valuation tree for n2+7

Olena Kozhushkina, Maila Bruca Hallare, Jane H. Long, Victor H. Moll, Jean-Claud Pedjeu, Bianca Thompson, Justin Trulen

Stephen F Austin State University

Research output: Contribution to journal › Article

Abstract

The 2-adic valuation of an integer x is the highest power of 2 whichdivides x. It is denoted by ν2(x). The goal of the present work is to describe thesequence {ν2(n2+ a)}for 1 6a 67. The first six cases are elementary. The lastcase considered here, namely a = 7, presents distinct challenges. It is shown herehow to represent this family of valuations in the form of an infinite binary tree,with two symmetric infinite branches.

Original language	Undefined/Unknown
Journal	Faculty Publications
State	Published - Jan 1 2020

Access to Document

http://scholarworks.sfasu.edu/mathandstats_facultypubs/29

Cite this

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title = "The valuation tree for n2+7",

abstract = "The 2-adic valuation of an integer x is the highest power of 2 whichdivides x. It is denoted by ν2(x). The goal of the present work is to describe thesequence {ν2(n2+ a)}for 1 6a 67. The first six cases are elementary. The lastcase considered here, namely a = 7, presents distinct challenges. It is shown herehow to represent this family of valuations in the form of an infinite binary tree,with two symmetric infinite branches.",

author = "Olena Kozhushkina and Hallare, {Maila Bruca} and Long, {Jane H.} and Moll, {Victor H.} and Jean-Claud Pedjeu and Bianca Thompson and Justin Trulen",

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day = "1",

language = "Undefined/Unknown",

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TY - JOUR

T1 - The valuation tree for n2+7

AU - Kozhushkina, Olena

AU - Hallare, Maila Bruca

AU - Long, Jane H.

AU - Moll, Victor H.

AU - Pedjeu, Jean-Claud

AU - Thompson, Bianca

AU - Trulen, Justin

PY - 2020/1/1

Y1 - 2020/1/1

N2 - The 2-adic valuation of an integer x is the highest power of 2 whichdivides x. It is denoted by ν2(x). The goal of the present work is to describe thesequence {ν2(n2+ a)}for 1 6a 67. The first six cases are elementary. The lastcase considered here, namely a = 7, presents distinct challenges. It is shown herehow to represent this family of valuations in the form of an infinite binary tree,with two symmetric infinite branches.

AB - The 2-adic valuation of an integer x is the highest power of 2 whichdivides x. It is denoted by ν2(x). The goal of the present work is to describe thesequence {ν2(n2+ a)}for 1 6a 67. The first six cases are elementary. The lastcase considered here, namely a = 7, presents distinct challenges. It is shown herehow to represent this family of valuations in the form of an infinite binary tree,with two symmetric infinite branches.

M3 - Article

JO - Faculty Publications

JF - Faculty Publications

ER -