Refinements of Lagrange's four-square theorem

A well-known theorem of Lagrange asserts that every nonnegative integer \(n\) can be written in the form \(a^2+b^2+c^2+d^2\), where \(a,b,c,d \in \mathbb{Z}\). We characterize the values assumed by \(a+b+c+d\) as we range over all such representations of \(n\).

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Bibliographic Details
Published in:arXiv.org 2017-03
Main Authors: Goldmakher, Leo, Pollack, Paul
Format: Article
Language:English
Subjects:
Theorems
Online Access:Get full text
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Summary:A well-known theorem of Lagrange asserts that every nonnegative integer \(n\) can be written in the form \(a^2+b^2+c^2+d^2\), where \(a,b,c,d \in \mathbb{Z}\). We characterize the values assumed by \(a+b+c+d\) as we range over all such representations of \(n\).
ISSN:2331-8422