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On a question of Sárkozy and Sós for bilinear forms

Autor
Cilleruelo, J.; Rue, J.
Tipus d'activitat
Article en revista
Revista
Bulletin of the London Mathematical Society
Data de publicació
2009-02-02
Volum
41
Número
2
Pàgina inicial
274
Pàgina final
280
Repositori
http://hdl.handle.net/2117/8374 Obrir en finestra nova
URL
http://www.uam.es/personal_pdi/ciencias/cillerue/Papers/On%20a%20question%20of%20Sarkozy%20and%20Sos.pdf Obrir en finestra nova
Resum
We prove that if 2 ≤ k1 ≤ k2, then there is no infinite sequence $\emph{A}$ of positive integers such that the representation function r(n)=#{(a, a'): n=$k{_1}a$ + $k{_2}a'$, a,a' ∊ $\emph{A}$} is constant for n large enough. This result completes previous work of Dirac and Moser for the special case $k_1$ = 1 and answers a question posed by Sárkozy and Sós.
Citació
Cilleruelo, J.; Rue, J. On a question of Sárkozy and Sós for bilinear forms. "Bulletin of the London Mathematical Society", 02 Febrer 2009, vol. 41, núm. 2, p. 274-280.
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants