Abstract
The set of the integers, nonnegative integers, resp. positive integers is denoted by ℤ, ℕ0 and ℕ. A, B, ... denote (finite or infinite) subsets of ℕ0, and their counting functions are denoted by A(n), B(n),... so that, e.g.,
Partially spported by Hungarian National Foundation for Scientific Research, Grant No. T 029759.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Balasubramanian, A note on a result of Erdős, Sárközy and Sós, Acta Arith., 49 (1987), 45–53.
G. Dombi, Additive properties of certain sets, Acta Arith., to appear.
P. Erdős, Problems and results in additive number theory, Colloque sur la Thèorie des Numbers (CBRM) (Bruxelles, 1956), 127–137.
P. Erdős and R. Freud, On Sidon-sequences and related problems, Mat. Lapok, 1 (1991), 1–44 (in Hungarian).
P. Erdős and A. Sárközy, Problems and results on additive properties of general sequences, I, Pacific J., 118 (1985), 347–357.
P. Erdős and A. Sárközy, Problems and results on additive properties of general sequences, II, Acta Math. Acad. Sci. Hungar., 48 (1986), 201–211.
P. Erdős, A. Sárközy and V. T. Sós, Problems and results on additive properties of general sequences, III, Studia Sci. Math. Hungar., 22 (1987), 53–63.
P. Erdős, A. Sárközy and V. T. Sós, Problems and results on additive properties of general sequences, IV, in: Number Theory, Proceedings, Ootacamund, India, 1984, Lecture Notes in Mathematics 1122, Springer-Verlag, 1985; 85–104.
P. Erdõs, A. Sárközy and V. T. Sós, Problems and results on additive properties of general sequences, V, Monatshefte Math., 102 (1986), 183–197.
P. Erdős, A. Sárközy and V. T. Sós, On a conjecture of Roth and some related problems, I., in: Irregularities of Partitions, eds. G. Halász and V. T. Sós, Algorithms and Combinatorics 8, Springer-Verlag, Berlin-Heidelberg-New York, 1989; 47–59.
P. Erdős, A. Sárközy and V. T. Sós, On additive properties of general sequences, Discrete Math., 136 (1994), 75–99.
P. Erdős, A. Sárközy and V. T. Sós, On sum sets of Sidon sets, I., J. Number Theory, 47 (1994), 329–347.
P. Erdős, A. Sárközy and V. T. Sós, On sum sets of Sidon sets, II., Israel J. Math., 90 (1995), 221–233.
G. Horváth, On an additive property of sequences of nonnegative integers, Periodica Math. Hungar., to appear.
Cs. Sándor, Range of bounded additive representation functions, Periodica Math. Hungar., 42 (2001), 169–177.
A. Sárközy, Unsolved problems in number theory, Periodica Math. Hungar., 42 (2001), 17–35.
A. Sárközy and V. T. Sós, On additive representation functions, in: The Mathematics of Paul Erdős, vol. I, eds. R. L. Graham and J. Nešetřil, Algorithms and Combinatorics 13, Springer-Verlag, 1997, 129–150.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to András Hajnal and Vera T. Sós on the occasion of their 70th birthday
Rights and permissions
Copyright information
© 2006 János Bolyai Mathematical Society and Springer Verlag
About this chapter
Cite this chapter
Sárközy, A. (2006). On the Number of Additive Representations of Integers. In: Győri, E., Katona, G.O.H., Lovász, L., Fleiner, T. (eds) More Sets, Graphs and Numbers. Bolyai Society Mathematical Studies, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32439-3_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-32439-3_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32377-8
Online ISBN: 978-3-540-32439-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)