2011/08/09 by Yan Li, Li, Yan, Lianrong Ma +1
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1108.1920
openalex publication_date 2011/08/09 · openalex created_date 2017/05/12 · openalex updated_date 2026/07/28
For m≥ 1, let 00 be fixed positive integers. Assume there exists a prime p and an integer t>0 such that pt| b0, but pt\nmid bi \rm for 1≤ i≤ m. Then, we prove that there is no infinite subset \mathcal A of positive integers, such that the number of solutions of the following equation n=b0(a0,1+...+a0,e0)+...+bm(am,1+...+am,rm), ai,j∈ \mathcal A is constant for n large enough. This result generalizes the recent result of Cilleruelo and Rué for bilinear case, and answers a question posed by Sárkozy and Sós.