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On a problem of Sárközy and Sós for multivariate linear forms

Author
Rue, J.; Spiegel, C.
Type of activity
Journal article
Journal
Electronic notes in discrete mathematics
Date of publication
2018-07-01
Volume
68
Number
July 2018
First page
101
Last page
106
DOI
https://doi.org/10.1016/j.endm.2018.06.018 Open in new window
Project funding
Discrete, geometric and random structures
Repository
http://hdl.handle.net/2117/121761 Open in new window
URL
https://www.sciencedirect.com/science/article/pii/S1571065318301094 Open in new window
Abstract
We prove that for pairwise co-prime numbers k1,...,kd = 2 there does not exist any infinite set of positive integers A such that the representation function rA(n) = #{(a1,...,ad) ¿ Ad : k1a1 + ... + kdad = n} becomes constant for n large enough. This result is a particular case of our main theorem, which poses a further step towards answering a question of S´ark¨ozy and S´os and widely extends a previous result of Cilleruelo and Ru´e for bivariate linear forms (Bull. of the London Math. Soc...
Citation
Rue, J., Spiegel, C. On a problem of Sárközy and Sós for multivariate linear forms. "Electronic notes in discrete mathematics", 1 Juliol 2018, vol. 68, núm. July 2018, p. 101-106.
Keywords
additive basis, additive combinatorics, representation functions
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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