Monochromatic sums of squares - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematische Zeitschrift Année : 2018

Monochromatic sums of squares

Résumé

For any integer let s(K) be the smallest integer such that in any colouring of the set of squares of the integers in K colours every large enough integer can be written as a sum of no more than s(K) squares, all of the same colour. A problem proposed by Sarkozy asks for optimal bounds for s(K) in terms of K. It is known by a result of Hegyvari and Hennecart that . In this article we show that . This improves on the bound , which is the best available upper bound for s(K).
Fichier non déposé

Dates et versions

hal-02060277 , version 1 (07-03-2019)

Identifiants

Citer

Gyan Prakash, D. S. Ramana, Olivier Ramaré. Monochromatic sums of squares. Mathematische Zeitschrift, 2018, 289 (1-2), pp.51-69. ⟨10.1007/s00209-017-1943-7⟩. ⟨hal-02060277⟩
41 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More