On a question of Sarkozy and Sos for bilinear forms

被引：11

作者：

Cilleruelo, Javier ^{[1
]}

Rue, Juanjo ^{[2
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] Univ Politecn Cataluna, Dept Matemat Aplicada 2, ES-08034 Barcelona, Spain

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2009年 / 41卷

关键词：

D O I：

10.1112/blms/bdn123

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that, if 2 <= k(1) <= k(2), then there is no infinite sequence of positive integers such that the representation function r(n) = #{(a, a'): n = k(1)a + k(2)a', a, a' is an element of } is constant for n large enough. This result completes the previous work of Dirac and Moser for the special case k(1) = 1 and answers a question posed by Sarkozy and Sos.

引用

页码：274 / 280

页数：7