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On polynomial representation functions for multilinear forms

2011/04/14 by Juanjo Rué, Rué, Juanjo
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Polynomial and algebraic computation #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1104.2716

Abstract

Given an infinite sequence of positive integers \cA, we prove that for every nonnegative integer k the number of solutions of the equation n=a1+...+ak, a1, ..., ak∈ \cA, 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 multilinear forms. Additionally, we obtain an Erdős-Fuchs type result for a wide variety of representation functions.

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