Resumen de On a problem of Sárközy and Sós for multivariate linear forms

Juanjo Rué Perna , Christoph Spiegel

• We prove that for pairwise co-prime numbers k1,…,kd≥2 there does not exist any infinite set of positive integers A such that the representation function rA(n)=#{(a1,…,ad)∈Ad:k1a1+⋯+kdad=n} becomes constant for n 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).