On polynomial representation functions for multivariate linear forms

نویسنده

Juanjo Rué

چکیده

Given an infinite sequence of positive integers A, we prove that for every nonnegative integer k the number of solutions of the equation n = a1 + · · ·+ak, a1, . . . , ak ∈ A, is not constant for n large enough. This result is a corollary of our main theorem, which partially answers a question of Sárközy and Sós on representation functions for multivariate linear forms. Additionally, we obtain an Erdős-Fuchs type result for a wide variety of representation functions.

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