Representation functions with different weights

• Autorzy: Quan-Hui Yang
• Języki publikacji: EN

Abstrakty

EN

For any given positive integer k, and any set A of nonnegative integers, let $r_{1,k}(A,n)$ denote the number of solutions of the equation n = a₁ + ka₂ with a₁,a₂ ∈ A. We prove that if k,l are multiplicatively independent integers, i.e., log k/log l is irrational, then there does not exist any set A ⊆ ℕ such that both $r_{1,k}(A,n) = r_{1,k}(ℕ ∖ A,n)$ and $r_{1,l}(A,n) = r_{1,l}(ℕ ∖ A,n)$ hold for all n ≥ n₀. We also pose a conjecture and two problems for further research.

Kategorie tematyczne

• 11B34: Representation functions
• 05A17: Partitions of integers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 137
• Numer: 1
• Strony: 1-6

Daty

wydano

2014

Twórcy

autor

Quan-Hui Yang

• School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Identyfikatory

DOI

10.4064/cm137-1-1