Sums of distinct integral squares in real quadratic fields

Kim, Byeong Moon; Park, Poo-Sung

doi:10.1016/j.crma.2011.03.019

Number Theory

Sums of distinct integral squares in real quadratic fields
[Sommes de carrés distincts dans lʼanneau des entiers dʼun corps quadratique réel]

Présenté par : Jean-Pierre Serre

Kim, Byeong Moon ¹ ; Park, Poo-Sung ²

¹ Department of Mathematics, Gangnung-Wonju National University, Gangneung Daehangno 120, Gangneung City, Gangwon Province, 210-702, Republic of Korea
² Department of Mathematics Education, Kyungnam University, Changwon, 631-701, Republic of Korea

Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 497-500.

Résumé
Abstract

Nous montrons que les entiers totalement positifs de normes suffisamment grandes sont des sommes de carrés distincts dans lʼanneau des entiers des corps réel quadratique.

We show that the elements of the ring of integers of real quadratic fields which are sums of integral squares are in fact sums of distinct squares, provided their norm is large enough.

Reçu le : 2010-05-11
Accepté le : 2011-03-22
Publié le : 2011-04-12

DOI : 10.1016/j.crma.2011.03.019

Affiliations des auteurs :

Kim, Byeong Moon ¹ ; Park, Poo-Sung ²

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     title = {Sums of distinct integral squares in real quadratic fields},
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Kim, Byeong Moon; Park, Poo-Sung. Sums of distinct integral squares in real quadratic fields. Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 497-500. doi : 10.1016/j.crma.2011.03.019. http://www.numdam.org/articles/10.1016/j.crma.2011.03.019/

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