On polynomial representation functions for multivariate linear forms
Rights accessOpen Access
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 S´ark¨ozy and S´os on representation functions for multivariate linear forms. Additionally, we obtain an Erd¿os-Fuchs type result for a wide variety of representation functions.
CitationRue, J. On polynomial representation functions for multivariate linear forms. "European journal of combinatorics", 01 Novembre 2013, vol. 34, núm. 8, p. 1429-1435.