no. 13-14
Number Theory
Sums of distinct integral squares in Q(5)
[Sommes de carrés distinctes dans l'anneau d'entiers de Q(5)]

Présenté par : Jean-Pierre Serre

Park, Poo-Sung1
1 School of Computational Sciences, Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul, 130-722, Korea
Comptes Rendus. Mathématique, Tome 346 (2008) no. 13-14, pp. 723-725.

Nous déterminons tous les entiers totalement positifs qui ne peuvent pas être représentés comme des sommes de carrés distincts d'entiers dans Q(5).

In this Note, we determine all the totally positive integers of Q(5) which cannot be represented as sums of distinct integral squares.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.05.008
Park, Poo-Sung 1

1 School of Computational Sciences, Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul, 130-722, Korea 
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Park, Poo-Sung. Sums of distinct integral squares in $ \mathbb{Q}(\sqrt{5})$. Comptes Rendus. Mathématique, Tome 346 (2008) no. 13-14, pp. 723-725. doi : 10.1016/j.crma.2008.05.008. http://www.numdam.org/articles/10.1016/j.crma.2008.05.008/

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[2] Kim, B.M. On nonvanishing sum of integral squares of Q(5), Kangweon-Kyungki Math. J., Volume 6 (1998) no. 2, pp. 299-302

[3] Maass, H. Über die Darstellung total positiver Zahlen des Körpers R(5) als Summe von drei Quadraten, Abh. Math. Sem. Hansischen Univ., Volume 14 (1941), pp. 185-191

[4] Siegel, C.L. Sums of mth powers of algebraic integers, Ann. of Math., Volume 46 (1945), pp. 313-339 (Ges. Abh. III, pp. 12–46)

[5] Sprague, R. Über Zerlegungen in ungleiche Quadratzahlen, Math. Z., Volume 51 (1949), pp. 289-290

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