Sums of distinct integral squares in real quadratic fields

Byeong Moon Kim; Poo-Sung Park

doi:10.1016/j.crma.2011.03.019

Number Theory

Sums of distinct integral squares in real quadratic fields

Presented by: Jean-Pierre Serre

Byeong Moon Kim ¹; Poo-Sung Park 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, Volume 349 (2011) no. 9-10, pp. 497-500.

Abstract
Résumé

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.

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.

Received: 2010-05-11
Accepted: 2011-03-22
Published online: 2011-04-12

DOI: 10.1016/j.crma.2011.03.019

Author's affiliations:

Byeong Moon Kim ¹; Poo-Sung Park 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

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Byeong Moon Kim; Poo-Sung Park. Sums of distinct integral squares in real quadratic fields. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 497-500. doi : 10.1016/j.crma.2011.03.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.019/

References
Cited by

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