On a problem of Sárközy and Sós for multivariate linear forms
Juanjo RuéUniversitat Politècnica de Catalunya, Barcelona, Spain
Christoph SpiegelUniversitat Politècnica de Catalunya, Barcelona, Spain
We prove that for pairwise co-prime numbers there does not exist any infinite set of positive integers such that the representation function becomes constant for large enough. This result is a particular case of our main theorem, which poses a further step towards answering a question of Sárközy and Sós and widely extends a previous result of Cilleruelo and Rué for bivariate linear forms (Bull. of the London Math. Society, 2009).
Cite this article
Juanjo Rué, Christoph Spiegel, On a problem of Sárközy and Sós for multivariate linear forms. Rev. Mat. Iberoam. 36 (2020), no. 7, pp. 2107–2119DOI 10.4171/RMI/1193