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On the Digits of Sumsets

Published online by Cambridge University Press:  20 November 2018

Christian Mauduit ,
Joël Rivat  and
András Sárközy
Christian Mauduit
Affiliation:
Université d'Aix-Marseille and Institut Universitaire de France, Institut de Mathématiques de Marseille, CNRS UMR 7373, 163, avenue de Luminy, Case 9, 13288 MARSEILLE Cedex 9, France e-mail: mauduit@iml.univ-mrs.fr
Joël Rivat
Affiliation:
Université d'Aix-Marseille, Institut de Mathématiques de Marseille, CNRS UMR 7373, 163, avenue de Luminy, Case 907, 13288 MARSEILLE Cedex 9, France e-mail: joel.rivat@univ-amu.fr
András Sárközy
Affiliation:
Eötvös Loránd University, Department of Algebra and Number Theory, H-1117 Budapest, Pázmány Péter sétány 1/c, Hungary e-mail: sarkozy@cs.elte.hu
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Abstract

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Let $\mathcal{A}$ and $\mathcal{B}$ be large subsets of $\{1,\,.\,.\,.\,,\,N\}$. We study the number of pairs $\left( a,b \right)\,\in \,\mathcal{A}\,\times \,\mathcal{B}$ such that the sum of binary digits of $a\,+\,b$ is fixed.

Keywords

11A6311B13sumsetdigits

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 3 , 01 June 2017 , pp. 595 - 612
Copyright
Copyright © Canadian Mathematical Society 2017

References

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