A Note on the Number of (k, l)-Sum-Free Sets

Abstract

A set A ⊆ N is (k, `)-sum-free, for k, ` ∈ N, k > `, if it contains no solutions to the equation x1 + · · ·+xk = y1 + · · ·+y`. Let ρ = ρ(k− `) be the smallest natural number not dividing k − `, and let r = rn, 0 ≤ r < ρ, be such that r ≡ n (mod ρ). The main result of this note says that if (k − `)/` is small in terms of ρ, then the number of (k, `)-sum… (More)

Topics

Figures and Tables

Sorry, we couldn't extract any figures or tables for this paper.