2012/01/19 by Lajos Hajdu, Hajdu, Lajos, R. Tijdeman +1
Computer Science · Mathematics · #11D85 #Analytic Number Theory Research #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1201.3991
openalex publication_date 2012/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let P be a finite set of at least two prime numbers, and A the set of positive integers that are products of powers of primes from P. Let F(k) denote the smallest positive integer which cannot be presented as sum of less than k terms of A. In a recent paper Nathanson asked to determine the properties of the function F(k), in particular to estimate its growth rate. In this paper we derive several results on F(k) and on the related function which denotes the smallest positive integer which cannot be presented as sum of less than k terms from the union of A and -A.