Title of article :
Partitions of Finite Nonnegative Integer Sets with Identical Representation Functions
Author/Authors :
Sun ، Cui-Fang Department of Mathematics - School of Mathematics and Statistics - Anhui Normal University , Pan ، Hao Department of Mathematics - School of Mathematics and Statistics - Anhui Normal University
Abstract :
LetNbe the set of all nonnegative integers. For S ⊆ Nand n ∈ N, let the representation function RS(n) denote the number of solutions of the equation n = s+s with s, s ∈ S and s s . In this paper,we determine the structure ofC, D ⊆ NwithC∪D = [0,m], C ∩ D = {r1, r2}, r1 r2 and 2 | r1 such that RC (n) = RD(n) for any nonnegative integer n.
Keywords :
Representation function , Thue–Morse sequence , Sárközy’s problem ,
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
